diff --git a/onnxruntime/contrib_ops/cpu/quantization/matmul_nbits_impl.cc b/onnxruntime/contrib_ops/cpu/quantization/matmul_nbits_impl.cc
index f92e59e990ba5..7e343d85f4048 100644
--- a/onnxruntime/contrib_ops/cpu/quantization/matmul_nbits_impl.cc
+++ b/onnxruntime/contrib_ops/cpu/quantization/matmul_nbits_impl.cc
@@ -41,8 +41,9 @@ void Dequantize4BitsKernelReOrder(
   T* output_i = output + out_y * out_cols + out_x;
   uint32_t quant_value = *(reinterpret_cast<const uint32_t*>(quant_data + element_offset / 2));
   const int remain_x = std::min(8, out_cols - out_x);
+  const int32_t* reorder_idx_with_off = reorder_idx + kb_idx * block_size + ((threadIdx_x * 8) & (block_size - 1));
   for (int i = 0; i < remain_x; i++) {
-    int32_t rid = reorder_idx ? reorder_idx[kb_idx * block_size + i] : kb_idx;
+    int32_t rid = reorder_idx ? reorder_idx_with_off[i] : kb_idx;
     T scale = *(scale_data + n_idx * scales_shape_x + rid);
     float zp_f = 8;
     if (zero_points) {
diff --git a/onnxruntime/contrib_ops/cuda/quantization/dequantize_blockwise.cu b/onnxruntime/contrib_ops/cuda/quantization/dequantize_blockwise.cu
index cd6593352008b..265adf22eeb61 100644
--- a/onnxruntime/contrib_ops/cuda/quantization/dequantize_blockwise.cu
+++ b/onnxruntime/contrib_ops/cuda/quantization/dequantize_blockwise.cu
@@ -23,7 +23,7 @@ namespace cuda {
 
 __device__ __forceinline__ void DequantizeEightElements(uint32_t values_quant, half scale, half zp, half* output) {
   half2 scale_half2 = {scale, scale};
-  half zp_adjust = -scale * __short2half_rn(zp);
+  half zp_adjust = -scale * zp;
   half2 zp_adjust2 = {zp_adjust, zp_adjust};
 
   alignas(16) half2 results[4];
@@ -83,8 +83,9 @@ __global__ void Dequantize4BitsKernelReOrder(
   int element_offset = group_id * block_size + ((threadIdx.x * 8) & (block_size - 1));
   T* output_i = output + element_offset;
   uint32_t quant_value = *(reinterpret_cast<const uint32_t*>(quant_data + element_offset / 2));
+  const int32_t* reorder_idx_with_off = reorder_idx + kb_idx * block_size + ((threadIdx.x * 8) & (block_size - 1));
   for (int i = 0; i < 8; i++) {
-    int32_t rid = reorder_idx[kb_idx * block_size + i];
+    int32_t rid = reorder_idx_with_off[i];
     T scale = *(scale_data + n_idx * scales_shape_x + rid);
     uint8_t zp = 8;
     if (zero_points) {
@@ -157,7 +158,7 @@ Status Dequantize4Bits(
   int groups_per_K = k / block_size;
   int total_groups = n * groups_per_K;  // total elemenets in quant_data
   int groups_per_grid = static_cast<int>(CeilDiv(total_groups, groups_per_threadblock));
-  if (!reorder_idx) {
+  if (!reorder_idx || std::is_same_v<ZeroT, T>) {
     Dequantize4BitsKernel<T, ZeroT><<<groups_per_grid, GridDim::maxThreadsPerBlock, 0, stream>>>(
         output,
         quant_data,