diff --git a/deepspeed/runtime/zero/stage3.py b/deepspeed/runtime/zero/stage3.py
index 9b7645261eae..b0a3ab778f2a 100644
--- a/deepspeed/runtime/zero/stage3.py
+++ b/deepspeed/runtime/zero/stage3.py
@@ -15,7 +15,7 @@
 from deepspeed.utils import logger
 from deepspeed.runtime.fp16.loss_scaler import CreateLossScaler
 from deepspeed.runtime.comm.coalesced_collectives import reduce_scatter_coalesced, all_to_all_quant_reduce
-from deepspeed.runtime.utils import inf, get_global_norm, is_model_parallel_parameter, get_only_unique_item
+from deepspeed.runtime.utils import inf, is_model_parallel_parameter, get_only_unique_item
 from deepspeed.runtime.zero.partition_parameters import *
 from deepspeed.runtime.zero.config import ZeroStageEnum
 from deepspeed.runtime.zero.offload_config import OffloadDeviceEnum
@@ -1413,7 +1413,7 @@ def complete_grad_norm_calculation_for_cpu_offload(self, params):
         err = torch.tensor(-1.0, device=inf_or_nan.device, dtype=torch.float)
         total_norm = inf_or_nan * err + inf_or_nan.logical_not() * total_norm
 
-        return total_norm
+        return total_norm.cpu()
 
     @instrument_w_nvtx
     def partition_grads(self, params_to_release: List[Parameter], grad_partitions: List[Tensor]) -> None:
@@ -2028,7 +2028,7 @@ def step(self, closure=None):
             return
 
         norm_groups = self._get_norm_groups()
-        scaled_global_grad_norm = get_global_norm(norm_list=norm_groups)
+        scaled_global_grad_norm = torch.linalg.norm(torch.stack(norm_groups))
 
         # Stash unscaled gradient norm
         self._global_grad_norm = scaled_global_grad_norm / self.loss_scale
@@ -2112,8 +2112,8 @@ def unscale_and_clip_grads(self, sub_group_id, total_norm):
         if self.clip_grad > 0.:
             # norm is in fact norm*scale
             clip = ((total_norm / self.loss_scale) + 1e-6) / self.clip_grad
-            if clip > 1:
-                combined_scale = clip * self.loss_scale
+            clip = torch.clamp(clip, min=1.0)
+            combined_scale = clip * self.loss_scale
 
         self.fp32_partitioned_groups_flat[sub_group_id].grad.mul_(1. / combined_scale)
 
diff --git a/tests/unit/runtime/zero/test_zero_offloadpp.py b/tests/unit/runtime/zero/test_zero_offloadpp.py
index 5bfec399e19f..8ae99e2237e2 100644
--- a/tests/unit/runtime/zero/test_zero_offloadpp.py
+++ b/tests/unit/runtime/zero/test_zero_offloadpp.py
@@ -43,6 +43,7 @@ def test(self, h_dim: int, n_layers: int) -> None:
         config_dict = {
             "train_batch_size": 256,
             "steps_per_print": 1,
+            "gradient_clipping": 1.0,
             "optimizer": {
                 "type": "Adam",
                 "params": {