diff --git a/tests/backend_test_base.py b/tests/backend_test_base.py
index b45f07c63..2adf7acea 100644
--- a/tests/backend_test_base.py
+++ b/tests/backend_test_base.py
@@ -91,7 +91,7 @@ def _run_backend(self, g, outputs, input_dict):
             raise ValueError("unknown backend")
         return y
 
-    def run_test_case(self, feed_dict, input_names_with_port, output_names_with_port, rtol=1e-07, atol=0.,
+    def run_test_case(self, feed_dict, input_names_with_port, output_names_with_port, rtol=1e-07, atol=1e-5,
                       convert_var_to_const=True, constant_fold=True, check_value=True, check_shape=False,
                       check_dtype=True, process_args=None, onnx_feed_dict=None, graph_validator=None):
         # optional - passed to process_tf_graph
diff --git a/tests/test_backend.py b/tests/test_backend.py
index 4e9b5de91..6bf9761cd 100644
--- a/tests/test_backend.py
+++ b/tests/test_backend.py
@@ -1118,6 +1118,7 @@ def test_sign(self):
             self._run_test_case([_OUTPUT], {_INPUT: x_val})
             tf.reset_default_graph()
 
+    @check_target("rs6", "onehot")
     def test_onehot0(self):
         x_val = np.array([0, 1, 2], dtype=np.int32)
         depth = 5
@@ -1138,6 +1139,7 @@ def test_onehot1(self):
         _ = tf.identity(x_, name=_TFOUTPUT)
         self._run_test_case([_OUTPUT], {_INPUT: x_val})
 
+    @check_target("rs6", "onehot")
     def test_onehot2(self):
         for axis in [-1, 0, 1]:
             tf.reset_default_graph()
@@ -1148,6 +1150,7 @@ def test_onehot2(self):
             _ = tf.identity(x_, name=_TFOUTPUT)
             self._run_test_case([_OUTPUT], {_INPUT: x_val})
 
+    @check_target("rs6", "onehot")
     @check_opset_min_version(9, "onehot")
     def test_onehot3(self):
         # rank 1
diff --git a/tests/test_optimizers.py b/tests/test_optimizers.py
index 15f218cd3..b10deee61 100644
--- a/tests/test_optimizers.py
+++ b/tests/test_optimizers.py
@@ -45,7 +45,7 @@ def run_and_compare(self, output_names_with_port, onnx_feed_dict, origin_proto,
             raise ValueError("only onnxruntime is supported to test transpose optimizer")
 
         for expected_val, actual_val in zip(expected, actual):
-            self.assertAllClose(expected_val, actual_val, rtol=rtol, atol=0.)
+            self.assertAllClose(expected_val, actual_val, rtol=rtol, atol=1e-5)
             self.assertEqual(expected_val.dtype, actual_val.dtype)
             self.assertEqual(expected_val.shape, actual_val.shape)
 
@@ -147,6 +147,21 @@ def test_transpose_with_shape(self):
         self.run_transpose_compare(["Z"], {"X": np.random.randn(2, 3, 4, 5).astype(np.float32)},
                                    model_proto, remaining_transpose_num=0)
 
+    def test_transpose_with_identity(self):
+        node1 = helper.make_node("Transpose", ["X"], ["Y"], perm=[0, 2, 3, 1], name="trans")
+        node2 = helper.make_node("Identity", ["Y"], ["Z"], name="identity")
+
+        graph = helper.make_graph(
+            [node1, node2],
+            "transpose_with_identity",
+            [helper.make_tensor_value_info("X", TensorProto.FLOAT, (2, 3, 4, 5))],
+            [helper.make_tensor_value_info("Z", TensorProto.FLOAT, (2, 4, 5, 3))],
+        )
+
+        model_proto = helper.make_model(graph, producer_name="onnx-tests")
+        self.run_transpose_compare(["Z"], {"X": np.random.randn(2, 3, 4, 5).astype(np.float32)},
+                                   model_proto, remaining_transpose_num=1)
+
     # Tranpose Optimizer Tests End
 
     # Identity Optimizer Tests Start
diff --git a/tf2onnx/optimizer/transpose_optimizer.py b/tf2onnx/optimizer/transpose_optimizer.py
index fd5ff2b55..4689f8f07 100644
--- a/tf2onnx/optimizer/transpose_optimizer.py
+++ b/tf2onnx/optimizer/transpose_optimizer.py
@@ -340,8 +340,13 @@ def _transpose_handler(self, trans, node):
             ops = self._g.get_nodes()
             self._g.replace_all_inputs(ops, node.output[0], trans.input[0])
 
+            shape = self._g.get_shape(node.output[0])
+            dtype = self._g.get_dtype(node.output[0])
             self._g.remove_node(trans.name)
             self._g.remove_node(node.name)
+            if node.output[0] in self._g.outputs:
+                self._g.make_node("Identity", [trans.input[0]],
+                                  outputs=node.output, shapes=[shape], dtypes=[dtype])
             return True
         return False
 
@@ -380,7 +385,8 @@ def _mul_handler(self, trans, node):
                 multiplier_input_id = i
                 multiplier_input_node = input_node
 
-        if not multiplier_input_node.is_const():
+        # node's inputs may come from one same node. if so the multiplier_input_node may be none
+        if multiplier_input_node is None or not multiplier_input_node.is_const():
             return False
         multiplier = multiplier_input_node.get_tensor_value(as_list=False)
 
@@ -408,6 +414,8 @@ def _mul_handler(self, trans, node):
         return False
 
     def _identity_handler(self, trans, node):
+        if node.output[0] in self._g.outputs:
+            return False
         ops = self._g.get_nodes()
         self._g.replace_all_inputs(ops, node.output[0], trans.output[0])
         self._g.remove_node(node.name)