diff --git a/src/interface/blas1_interface.hpp b/src/interface/blas1_interface.hpp
index 866588d68..d4393159e 100644
--- a/src/interface/blas1_interface.hpp
+++ b/src/interface/blas1_interface.hpp
@@ -332,10 +332,10 @@ typename sb_handle_t::event_t _nrm2(
   const auto nWG = 2 * localSize;
   auto assignOp =
       make_assign_reduction<AddOperator>(rs, prdOp, localSize, localSize * nWG);
-  auto ret0 = sb_handle.execute(assignOp);
+  auto ret0 = sb_handle.execute(assignOp, _dependencies);
   auto sqrtOp = make_op<UnaryOp, SqrtOperator>(rs);
   auto assignOpFinal = make_op<Assign>(rs, sqrtOp);
-  auto ret1 = sb_handle.execute(assignOpFinal, _dependencies);
+  auto ret1 = sb_handle.execute(assignOpFinal, ret0);
   return blas::concatenate_vectors(ret0, ret1);
 }
 
diff --git a/src/interface/blas2_interface.hpp b/src/interface/blas2_interface.hpp
index 21dae4b34..acd7fe736 100644
--- a/src/interface/blas2_interface.hpp
+++ b/src/interface/blas2_interface.hpp
@@ -661,8 +661,8 @@ typename sb_handle_t::event_t _tbmv_impl(
                                      global_size, _dependencies);
 
   auto assignOp = make_op<Assign>(vx, vres);
-  auto ret = concatenate_vectors(
-      tbmvEvent, sb_handle.execute(assignOp, local_range, _dependencies));
+  auto assignEvent = sb_handle.execute(assignOp, local_range, tbmvEvent);
+  auto ret = concatenate_vectors(tbmvEvent, assignEvent);
 
   blas::helper::enqueue_deallocate(ret, res_buffer, sb_handle.get_queue());
 
diff --git a/test/unittest/CMakeLists.txt b/test/unittest/CMakeLists.txt
index f76b6218c..c4b860432 100644
--- a/test/unittest/CMakeLists.txt
+++ b/test/unittest/CMakeLists.txt
@@ -39,6 +39,7 @@ set(SYCL_UNITTEST_SRCS
   ${SYCLBLAS_UNITTEST}/blas1/blas1_rotmg_test.cpp
   ${SYCLBLAS_UNITTEST}/blas1/blas1_rotg_test.cpp
   ${SYCLBLAS_UNITTEST}/blas1/blas1_sdsdot_test.cpp
+  ${SYCLBLAS_UNITTEST}/blas1/blas1_nrm2_test.cpp
   # # Blas 2 tests
   ${SYCLBLAS_UNITTEST}/blas2/blas2_gbmv_test.cpp
   ${SYCLBLAS_UNITTEST}/blas2/blas2_gemv_test.cpp
@@ -72,7 +73,6 @@ if(is_computecpp)
     # Blas 1 tests
     ${SYCLBLAS_UNITTEST}/blas1/blas1_swap_test.cpp
     ${SYCLBLAS_UNITTEST}/blas1/blas1_dot_test.cpp
-    ${SYCLBLAS_UNITTEST}/blas1/blas1_nrm2_test.cpp
     ${SYCLBLAS_UNITTEST}/blas1/blas1_iamax_test.cpp
     ${SYCLBLAS_UNITTEST}/blas1/blas1_iamin_test.cpp
     # Blas 2 tests
diff --git a/test/unittest/blas1/blas1_nrm2_test.cpp b/test/unittest/blas1/blas1_nrm2_test.cpp
index 4efd61725..383fab54c 100644
--- a/test/unittest/blas1/blas1_nrm2_test.cpp
+++ b/test/unittest/blas1/blas1_nrm2_test.cpp
@@ -26,7 +26,7 @@
 #include "blas_test.hpp"
 
 template <typename scalar_t>
-using combination_t = std::tuple<std::string, api_type, int, int>;
+using combination_t = std::tuple<std::string, api_type, int, int, scalar_t>;
 
 template <typename scalar_t, helper::AllocType mem_alloc>
 void run_test(const combination_t<scalar_t> combi) {
@@ -34,27 +34,39 @@ void run_test(const combination_t<scalar_t> combi) {
   api_type api;
   index_t size;
   index_t incX;
-  std::tie(alloc, api, size, incX) = combi;
+  scalar_t unused;
+  std::tie(alloc, api, size, incX, unused) = combi;
 
+  auto vector_size = size * std::abs(incX);
   // Input vectors
-  std::vector<scalar_t> x_v(size * incX);
+  std::vector<scalar_t> x_v(vector_size);
   fill_random(x_v);
 
   // Output scalar
   scalar_t out_s = 10.0;
+  scalar_t out_cpu_s = 20.0;
 
   // Reference implementation
-  auto out_cpu_s = reference_blas::nrm2(size, x_v.data(), incX);
+  if (incX < 0) {
+    // Some reference implementations of BLAS do not support negative
+    // increments for nrm2. To simulate what is specified in the
+    // oneAPI spec, invert the vector and use a positive increment.
+    std::vector<scalar_t> x_v_inv(vector_size);
+    std::reverse_copy(x_v.begin(), x_v.end() + (incX + 1), x_v_inv.begin());
+    out_cpu_s = reference_blas::nrm2(size, x_v_inv.data(), -incX);
+  } else {
+    out_cpu_s = reference_blas::nrm2(size, x_v.data(), incX);
+  }
 
   // SYCL implementation
   auto q = make_queue();
   blas::SB_Handle sb_handle(q);
 
   // Iterators
-  auto gpu_x_v = blas::helper::allocate<mem_alloc, scalar_t>(size * incX, q);
+  auto gpu_x_v = blas::helper::allocate<mem_alloc, scalar_t>(vector_size, q);
 
   auto copy_x =
-      blas::helper::copy_to_device(q, x_v.data(), gpu_x_v, size * incX);
+      blas::helper::copy_to_device(q, x_v.data(), gpu_x_v, vector_size);
 
   if (api == api_type::async) {
     auto gpu_out_s = blas::helper::allocate<mem_alloc, scalar_t>(1, q);
@@ -84,7 +96,8 @@ void run_test(const combination_t<scalar_t> combi) {
   api_type api;
   index_t size;
   index_t incX;
-  std::tie(alloc, api, size, incX) = combi;
+  scalar_t unused;
+  std::tie(alloc, api, size, incX, unused) = combi;
 
   if (alloc == "usm") {  // usm alloc
 #ifdef SB_ENABLE_USM
@@ -98,12 +111,12 @@ void run_test(const combination_t<scalar_t> combi) {
 }
 template <typename scalar_t>
 const auto combi =
-    ::testing::Combine(::testing::Values("usm", "buf"),  // allocation type
+    ::testing::Combine(::testing::Values("usm", "buf"),    // allocation type
                        ::testing::Values(api_type::async,
                                          api_type::sync),  // Api
                        ::testing::Values(11, 1002),        // size
-                       ::testing::Values(1, 4)             // incX
-    );
+                       ::testing::Values(1, 4, -3),        // incX
+                       ::testing::Values(scalar_t{1}));
 
 template <class T>
 static std::string generate_name(
@@ -111,7 +124,8 @@ static std::string generate_name(
   std::string alloc;
   api_type api;
   int size, incX;
-  BLAS_GENERATE_NAME(info.param, alloc, api, size, incX);
+  T unused;
+  BLAS_GENERATE_NAME(info.param, alloc, api, size, incX, unused);
 }
 
 BLAS_REGISTER_TEST_ALL(Nrm2, combination_t, combi, generate_name);