diff --git a/frame/compat/bla_gemm.c b/frame/compat/bla_gemm.c
index 557b3f202..044cdf9bb 100644
--- a/frame/compat/bla_gemm.c
+++ b/frame/compat/bla_gemm.c
@@ -666,8 +666,7 @@ void zgemm_
 		sqp_on = true;
 	}
 #endif
-	if( ( ( blis_transa == BLIS_TRANSPOSE ) || ( blis_transa == BLIS_NO_TRANSPOSE ) )
-		&& ( blis_transb == BLIS_NO_TRANSPOSE) && (sqp_on == true))
+	if( ( blis_transb == BLIS_NO_TRANSPOSE) && ( sqp_on == true ) )
 	{
 		//sqp algo is found better for n > 40
 		if(bli_gemm_sqp(&alphao, &ao, &bo, &betao, &co, NULL, NULL)==BLIS_SUCCESS)
diff --git a/kernels/zen/3/bli_gemm_sqp.c b/kernels/zen/3/bli_gemm_sqp.c
index 1622c551c..ceab622bf 100644
--- a/kernels/zen/3/bli_gemm_sqp.c
+++ b/kernels/zen/3/bli_gemm_sqp.c
@@ -40,16 +40,31 @@
 #define BLIS_LOADFIRST 0
 #define MEM_ALLOC 1//malloc performs better than bli_malloc.
 
+#define SET_TRANS(X,Y)\
+    Y = BLIS_NO_TRANSPOSE;\
+    if(bli_obj_has_trans( a ))\
+    {\
+        Y = BLIS_TRANSPOSE;\
+        if(bli_obj_has_conj(a))\
+        {\
+            Y = BLIS_CONJ_TRANSPOSE;\
+        }\
+    }\
+    else if(bli_obj_has_conj(a))\
+    {\
+        Y = BLIS_CONJ_NO_TRANSPOSE;\
+    }
+
 //Macro for 3m_sqp n loop
 #define BLI_SQP_ZGEMM_N(MX)\
     int j=0;\
     for(; j<=(n-nx); j+= nx)\
     {\
-        status = bli_sqp_zgemm_m8( m, nx, k, a, lda, b+(j*ldb), ldb, c+(j*ldc), ldc, alpha_real, beta_real, isTransA, MX,  p_istart, kx, &mem_3m_sqp);\
+        status = bli_sqp_zgemm_m8( m, nx, k, a, lda, b+(j*ldb), ldb, c+(j*ldc), ldc, alpha_real, beta_real, transa, MX,  p_istart, kx, &mem_3m_sqp);\
     }\
     if(j<n)\
     {\
-        status = bli_sqp_zgemm_m8( m, n-j, k, a, lda, b+(j*ldb), ldb, c+(j*ldc), ldc, alpha_real, beta_real, isTransA, MX,  p_istart, kx, &mem_3m_sqp);\
+        status = bli_sqp_zgemm_m8( m, n-j, k, a, lda, b+(j*ldb), ldb, c+(j*ldc), ldc, alpha_real, beta_real, transa, MX,  p_istart, kx, &mem_3m_sqp);\
     }
 
 //Macro for sqp_dgemm n loop
@@ -135,7 +150,7 @@ BLIS_INLINE err_t bli_sqp_zgemm( gint_t m,
                             guint_t ldc,
                             double alpha,
                             double beta,
-                            bool isTransA,
+                            trans_t transa,
                             dim_t nt);
 
 BLIS_INLINE err_t bli_sqp_dgemm( gint_t m,
@@ -181,7 +196,7 @@ err_t bli_gemm_sqp
         return BLIS_INVALID_ROW_STRIDE;
     }
 
-    if(bli_obj_has_conj(a) || bli_obj_has_conj(b))
+    if(bli_obj_has_conj(b))
     {
         return BLIS_NOT_YET_IMPLEMENTED;
     }
@@ -216,6 +231,9 @@ err_t bli_gemm_sqp
         isTransA = true;
     }
 
+    trans_t transa = BLIS_NO_TRANSPOSE;
+    SET_TRANS(a,transa)
+
     dim_t nt = bli_thread_get_num_threads(); // get number of threads
 
     double* ap     = ( double* )bli_obj_buffer( a );
@@ -237,7 +255,7 @@ err_t bli_gemm_sqp
             return BLIS_NOT_YET_IMPLEMENTED;
         }
         //printf("zsqp ");
-        return bli_sqp_zgemm( m, n, k, ap, lda, bp, ldb, cp, ldc, alpha_real, beta_real, isTransA, nt);
+        return bli_sqp_zgemm( m, n, k, ap, lda, bp, ldb, cp, ldc, alpha_real, beta_real, transa, nt);
     }
     else if(dt == BLIS_DOUBLE)
     {
@@ -254,6 +272,8 @@ err_t bli_gemm_sqp
             return BLIS_NOT_YET_IMPLEMENTED;
         }
         //printf("dsqp ");
+        // dgemm case only transpose or no-transpose is handled.
+        // conjugate_transpose and conjugate no transpose are not applicable.
         return bli_sqp_dgemm( m, n, k, ap, lda, bp, ldb, cp, ldc, *alpha_cast, *beta_cast, isTransA, nt);
     }
 
@@ -627,7 +647,7 @@ BLIS_INLINE void bli_sqp_zgemm_kx(  gint_t m,
                                     guint_t ldb,
                                     double* c,
                                     guint_t ldc,
-                                    bool isTransA,
+                                    trans_t transa,
                                     double alpha,
                                     double beta,
                                     gint_t mx,
@@ -653,7 +673,7 @@ BLIS_INLINE void bli_sqp_zgemm_kx(  gint_t m,
     double* pas = as;
 
     /* a matrix real and imag packing and compute. */
-    bli_3m_sqp_packA_real_imag_sum(a, i, kx+p, lda, par, pai, pas, isTransA, mx, p);
+    bli_3m_sqp_packA_real_imag_sum(a, i, kx+p, lda, par, pai, pas, transa, mx, p);
 
     double* pcr = cr;
     double* pci = ci;
@@ -874,7 +894,7 @@ BLIS_INLINE err_t bli_sqp_zgemm_m8( gint_t m,
                                     guint_t ldc,
                                     double alpha,
                                     double beta,
-                                    bool isTransA,
+                                    trans_t transa,
                                     gint_t mx,
                                     gint_t* p_istart,
                                     gint_t kx,
@@ -926,14 +946,14 @@ BLIS_INLINE err_t bli_sqp_zgemm_m8( gint_t m,
         for(; p <= (k-kx); p += kx)
         {
             bli_sqp_zgemm_kx(m, n, kx, p, a, lda, k, c, ldc,
-                            isTransA, alpha, beta, mx, i, ar, ai, as,
+                            transa, alpha, beta, mx, i, ar, ai, as,
                             br + p, bi + p, bs + p, cr, ci, w, a_aligned);
         }// k loop end
 
         if(p<k)
         {
             bli_sqp_zgemm_kx(m, n, (k - p), p, a, lda, k, c, ldc,
-                             isTransA, alpha, beta, mx, i, ar, ai, as,
+                             transa, alpha, beta, mx, i, ar, ai, as,
                             br + p, bi + p, bs + p, cr, ci, w, a_aligned);
         }
 #else//kloop
@@ -946,7 +966,7 @@ BLIS_INLINE err_t bli_sqp_zgemm_m8( gint_t m,
         double* pas = as;
 
         /* a matrix real and imag packing and compute. */
-        bli_3m_sqp_packA_real_imag_sum(a, i, k, lda, par, pai, pas, isTransA, mx, 0);
+        bli_3m_sqp_packA_real_imag_sum(a, i, k, lda, par, pai, pas, transa, mx, 0);
 
         double* pcr = cr;
         double* pci = ci;
@@ -1035,7 +1055,7 @@ BLIS_INLINE err_t bli_sqp_zgemm(gint_t m,
                                 guint_t ldc,
                                 double alpha_real,
                                 double beta_real,
-                                bool isTransA,
+                                trans_t transa,
                                 dim_t nt)
 {
     gint_t istart = 0;
@@ -1078,7 +1098,7 @@ BLIS_INLINE err_t bli_sqp_zgemm(gint_t m,
         kx = k;
     }
     // for tn case there is a bug in handling k parts. To be fixed.
-    if(isTransA==true)
+    if(transa!=BLIS_NO_TRANSPOSE)
     {
         kx = k;
     }
diff --git a/kernels/zen/3/bli_gemm_sqp_kernels.c b/kernels/zen/3/bli_gemm_sqp_kernels.c
index 4762fb831..9cac5e83e 100644
--- a/kernels/zen/3/bli_gemm_sqp_kernels.c
+++ b/kernels/zen/3/bli_gemm_sqp_kernels.c
@@ -1412,19 +1412,18 @@ void bli_3m_sqp_packA_real_imag_sum(double *pa,
                                     double *par,
                                     double *pai,
                                     double *pas,
-                                    bool isTransA,
+                                    trans_t transa,
                                     gint_t mx,
                                     gint_t p)
 {
     __m256d av0, av1, av2, av3;
-    __m256d tv0, tv1, sum;
+    __m256d tv0, tv1, sum, zerov;
     gint_t poffset = p;
 #if KLP
-    //k = p + k;
 #endif
     if(mx==8)
     {
-        if(isTransA==false)
+        if(transa == BLIS_NO_TRANSPOSE)
         {
             pa = pa +i;
 #if KLP
@@ -1432,7 +1431,6 @@ void bli_3m_sqp_packA_real_imag_sum(double *pa,
 #else
             p = 0;
 #endif
-            //printf("packA from p_%d to p_%d \n", p, k);
             for (; p < k; p += 1)
             {
                 //for (int ii = 0; ii < MX8 * 2; ii += 2) //real + imag : Rkernel needs 8 elements each.
@@ -1462,12 +1460,51 @@ void bli_3m_sqp_packA_real_imag_sum(double *pa,
                 pa = pa + lda;
             }
         }
-        else
+        else if(transa == BLIS_CONJ_NO_TRANSPOSE)
+        {
+            zerov = _mm256_setzero_pd();
+            pa = pa +i;
+#if KLP
+            pa = pa + (p*lda);
+#else
+            p = 0;
+#endif
+            for (; p < k; p += 1)
+            {
+                //for (int ii = 0; ii < MX8 * 2; ii += 2) //real + imag : Rkernel needs 8 elements each.
+                av0 = _mm256_loadu_pd(pa);
+                av1 = _mm256_loadu_pd(pa+4);
+                av2 = _mm256_loadu_pd(pa+8);
+                av3 = _mm256_loadu_pd(pa+12);
+
+                tv0 = _mm256_permute2f128_pd(av0, av1, 0x20);
+                tv1 = _mm256_permute2f128_pd(av0, av1, 0x31);
+                av0 = _mm256_unpacklo_pd(tv0, tv1);
+                av1 = _mm256_unpackhi_pd(tv0, tv1);
+                av1 = _mm256_sub_pd(zerov,av1);//negate imaginary component
+                sum = _mm256_add_pd(av0, av1);
+                _mm256_storeu_pd(par, av0); par += 4;
+                _mm256_storeu_pd(pai, av1); pai += 4;
+                _mm256_storeu_pd(pas, sum); pas += 4;
+
+                tv0 = _mm256_permute2f128_pd(av2, av3, 0x20);
+                tv1 = _mm256_permute2f128_pd(av2, av3, 0x31);
+                av2 = _mm256_unpacklo_pd(tv0, tv1);
+                av3 = _mm256_unpackhi_pd(tv0, tv1);
+                av3 = _mm256_sub_pd(zerov,av3);//negate imaginary component
+                sum = _mm256_add_pd(av2, av3);
+                _mm256_storeu_pd(par, av2); par += 4;
+                _mm256_storeu_pd(pai, av3); pai += 4;
+                _mm256_storeu_pd(pas, sum); pas += 4;
+
+                pa = pa + lda;
+            }
+        }
+        else if(transa == BLIS_TRANSPOSE)
         {
             gint_t idx = (i/2) * lda;
             pa = pa + idx;
 #if KLP
-            //pa = pa + p;
 #else
             p = 0;
 #endif
@@ -1527,18 +1564,79 @@ void bli_3m_sqp_packA_real_imag_sum(double *pa,
                 }
             }
         }
-    }   //mx==8
-    else//mx==1
-    {
-        if(isTransA==false)
+        else if(transa == BLIS_CONJ_TRANSPOSE)
         {
-            pa = pa + i;
+            gint_t idx = (i/2) * lda;
+            pa = pa + idx;
+#if KLP
+#else
+            p = 0;
+#endif
+            //A conjugate Transpose case:
+            for (gint_t ii = 0; ii < BLIS_MX8 ; ii++)
+            {
+                gint_t idx = ii * lda;
+                gint_t sidx;
+                gint_t pidx = 0;
+                gint_t max_k = (k*2) - 8;
+                for (p = poffset; p <= max_k; p += 8)
+                {
+                    double ar0_ = *(pa + idx + p);
+                    double ai0_ = -(*(pa + idx + p + 1));
+
+                    double ar1_ = *(pa + idx + p + 2);
+                    double ai1_ = -(*(pa + idx + p + 3));
+
+                    double ar2_ = *(pa + idx + p + 4);
+                    double ai2_ = -(*(pa + idx + p + 5));
+
+                    double ar3_ = *(pa + idx + p + 6);
+                    double ai3_ = -(*(pa + idx + p + 7));
+
+                    sidx = (pidx/2) * BLIS_MX8;
+                    *(par + sidx + ii) = ar0_;
+                    *(pai + sidx + ii) = ai0_;
+                    *(pas + sidx + ii) = ar0_ + ai0_;
+
+                    sidx = ((pidx+2)/2) * BLIS_MX8;
+                    *(par + sidx + ii) = ar1_;
+                    *(pai + sidx + ii) = ai1_;
+                    *(pas + sidx + ii) = ar1_ + ai1_;
+
+                    sidx = ((pidx+4)/2) * BLIS_MX8;
+                    *(par + sidx + ii) = ar2_;
+                    *(pai + sidx + ii) = ai2_;
+                    *(pas + sidx + ii) = ar2_ + ai2_;
+
+                    sidx = ((pidx+6)/2) * BLIS_MX8;
+                    *(par + sidx + ii) = ar3_;
+                    *(pai + sidx + ii) = ai3_;
+                    *(pas + sidx + ii) = ar3_ + ai3_;
+                    pidx += 8;
+                }
+
+                for (; p < (k*2); p += 2)
+                {
+                    double ar_ = *(pa + idx + p);
+                    double ai_ = -(*(pa + idx + p + 1));
+                    gint_t sidx = (pidx/2) * BLIS_MX8;
+                    *(par + sidx + ii) = ar_;
+                    *(pai + sidx + ii) = ai_;
+                    *(pas + sidx + ii) = ar_ + ai_;
+                    pidx += 2;
+                }
+            }
+        }
+    }   //mx==8
+    else//mx==1
+    {
+        if(transa == BLIS_NO_TRANSPOSE)
+        {
+            pa = pa + i;
 #if KLP
-            //pa = pa + (p*lda); done below.. not needed
 #else
             p = 0;
 #endif
-            //printf(" packAx1 from p_%d to p_%d ",p,k-1);
             //A No transpose case:
             for (; p < k; p += 1)
             {
@@ -1554,12 +1652,33 @@ void bli_3m_sqp_packA_real_imag_sum(double *pa,
                 }
             }
         }
-        else
+        else if(transa == BLIS_CONJ_NO_TRANSPOSE)
+        {
+            pa = pa + i;
+#if KLP
+#else
+            p = 0;
+#endif
+            //A conjuate No transpose case:
+            for (; p < k; p += 1)
+            {
+                gint_t idx = p * lda;
+                for (gint_t ii = 0; ii < (mx*2) ; ii += 2)
+                { //real + imag : Rkernel needs 8 elements each.
+                    double ar_ = *(pa + idx + ii);
+                    double ai_ = -(*(pa + idx + ii + 1));// conjugate: negate imaginary component
+                    *par = ar_;
+                    *pai = ai_;
+                    *pas = ar_ + ai_;
+                    par++; pai++; pas++;
+                }
+            }
+        }
+        else if(transa == BLIS_TRANSPOSE)
         {
             gint_t idx = (i/2) * lda;
             pa = pa + idx;
 #if KLP
-            //pa = pa + p; done below.. not needed
 #else
             p = 0;
 #endif
@@ -1583,6 +1702,34 @@ void bli_3m_sqp_packA_real_imag_sum(double *pa,
                 }
             }
         }
+        else if(transa == BLIS_CONJ_TRANSPOSE)
+        {
+            gint_t idx = (i/2) * lda;
+            pa = pa + idx;
+#if KLP
+#else
+            p = 0;
+#endif
+            //A Transpose case:
+            for (gint_t ii = 0; ii < mx ; ii++)
+            {
+                gint_t idx = ii * lda;
+                gint_t sidx;
+                gint_t pidx = 0;
+                for (p = poffset;p < (k*2); p += 2)
+                {
+                    double ar0_ = *(pa + idx + p);
+                    double ai0_ = -(*(pa + idx + p + 1));
+
+                    sidx = (pidx/2) * mx;
+                    *(par + sidx + ii) = ar0_;
+                    *(pai + sidx + ii) = ai0_;
+                    *(pas + sidx + ii) = ar0_ + ai0_;
+                    pidx += 2;
+
+                }
+            }
+        }
     }//mx==1
 }
 
diff --git a/kernels/zen/3/bli_gemm_sqp_kernels.h b/kernels/zen/3/bli_gemm_sqp_kernels.h
index 5d5405e0b..588981fad 100644
--- a/kernels/zen/3/bli_gemm_sqp_kernels.h
+++ b/kernels/zen/3/bli_gemm_sqp_kernels.h
@@ -62,4 +62,4 @@ void bli_prepackA_1(double* pa, double* aPacked, gint_t k, guint_t lda, bool isT
 /* Pack real and imaginary parts in separate buffers and also multipy with multiplication factor */
 void bli_3m_sqp_packC_real_imag(double* pb, guint_t n, guint_t k, guint_t ldb, double* pbr, double* pbi, double mul, gint_t mx);
 void bli_3m_sqp_packB_real_imag_sum(double* pb, guint_t n, guint_t k, guint_t ldb, double* pbr, double* pbi, double* pbs, double mul, gint_t mx);
-void bli_3m_sqp_packA_real_imag_sum(double *pa, gint_t i, guint_t k, guint_t lda, double *par, double *pai, double *pas, bool isTransA, gint_t mx, gint_t p);
\ No newline at end of file
+void bli_3m_sqp_packA_real_imag_sum(double *pa, gint_t i, guint_t k, guint_t lda, double *par, double *pai, double *pas, trans_t transa, gint_t mx, gint_t p);
\ No newline at end of file