diff --git a/include/ck_tile/ops/fmha/block/block_tile_window_navigator.hpp b/include/ck_tile/ops/fmha/block/block_tile_window_navigator.hpp
index 19c72f86cc..b1b67d3ba4 100644
--- a/include/ck_tile/ops/fmha/block/block_tile_window_navigator.hpp
+++ b/include/ck_tile/ops/fmha/block/block_tile_window_navigator.hpp
@@ -140,10 +140,12 @@ struct PagedTileWindowNavigator
     }
 
     template <typename TileWindow>
-    CK_TILE_HOST_DEVICE bool is_closs_block(const TileWindow& tile_window) const
+    CK_TILE_HOST_DEVICE bool is_cross_block(index_t block_index,
+                                            const TileWindow& tile_window) const
     {
-        return page_block_size < (tile_window.get_window_origin().at(number<VirtualDim>{}) +
-                                  tile_window.get_window_lengths().at(number<VirtualDim>{}));
+        const index_t origin = tile_window.get_window_origin().at(number<VirtualDim>{});
+        const index_t length = tile_window.get_window_lengths().at(number<VirtualDim>{});
+        return (block_index < num_blocks - 1) && (page_block_size < origin + length);
     }
 
     template <typename TileWindow>
diff --git a/include/ck_tile/ops/fmha/pipeline/block_fmha_fwd_appendkv_pipeline.hpp b/include/ck_tile/ops/fmha/pipeline/block_fmha_fwd_appendkv_pipeline.hpp
index c9d8ef9a8f..a04e4101b0 100644
--- a/include/ck_tile/ops/fmha/pipeline/block_fmha_fwd_appendkv_pipeline.hpp
+++ b/include/ck_tile/ops/fmha/pipeline/block_fmha_fwd_appendkv_pipeline.hpp
@@ -151,9 +151,8 @@ struct BlockFmhaFwdAppendKVPipeline
             if constexpr(kIsPagedKV)
             {
                 store_tile(k_dram_block_window, knew_tile);
-
                 // write tile to another block if nesscary
-                if(k_tile_navigator.is_closs_block(k_dram_block_window))
+                if(k_tile_navigator.is_cross_block(i_block0, k_dram_block_window))
                 {
                     k_tile_navigator.move_to_block(i_block0, k_dram_block_window, i_block0 + 1);
                     store_tile(k_dram_block_window, knew_tile);
@@ -176,9 +175,8 @@ struct BlockFmhaFwdAppendKVPipeline
             if constexpr(kIsPagedKV)
             {
                 store_tile(v_dram_block_window, vnew_tile);
-
                 // write tile to another block if nesscary
-                if(v_tile_navigator.is_closs_block(v_dram_block_window))
+                if(v_tile_navigator.is_cross_block(i_block1, v_dram_block_window))
                 {
                     v_tile_navigator.move_to_block(i_block1, v_dram_block_window, i_block1 + 1);
                     store_tile(v_dram_block_window, vnew_tile);