diff --git a/tf2onnx/rewriter/random_normal_rewriter.py b/tf2onnx/rewriter/random_normal_rewriter.py
index 6d106907e..3691b5f00 100644
--- a/tf2onnx/rewriter/random_normal_rewriter.py
+++ b/tf2onnx/rewriter/random_normal_rewriter.py
@@ -33,16 +33,22 @@ def rewrite_random_normal(g, ops):
         match_results = list(matcher.match_ops(ops))
         for match in match_results:
             output = match.get_op('output')
-            if output.type == 'Add':
+            input2 = match.get_op('input2')
+            is_output = False
+            for output_name in g.outputs:
+                # input2 and output can not be output node.
+                if input2.name in output_name or output.name in output_name:
+                    is_output = True
+                    break
+            if is_output:
+                continue
+            if output.type == 'Add' and input2.type == 'Mul':
                 # pattern 1
                 mean = output.inputs[1].get_tensor_value()
+                scale = input2.inputs[1].get_tensor_value()
             else:
                 # pattern 2
                 mean = 0.0
-            input2 = match.get_op('input2')
-            if input2.type == 'Mul':
-                scale = input2.inputs[1].get_tensor_value()
-            else:
                 scale = 1.0
             dtype = g.get_dtype(output.output[0])
             op_name = utils.make_name("RandomNormal")
diff --git a/tf2onnx/tf_loader.py b/tf2onnx/tf_loader.py
index 7269a26e0..d9d72a8dc 100644
--- a/tf2onnx/tf_loader.py
+++ b/tf2onnx/tf_loader.py
@@ -687,6 +687,10 @@ def tf_optimize_grappler(input_names, output_names, graph_def):
         'constfold', 'function'
     ]
 
+    if is_tf2():
+        # add for tf2.x lstm optimization.
+        rewrite_options.optimizers.append('dependency')
+
     if Version(tf.__version__) >= Version("2.5"):
         # This flag disables folding QDQ nodes around constants in the network (eg: around conv/FC weights)
         rewrite_options.experimental_disable_folding_quantization_emulation = True
@@ -771,8 +775,8 @@ def toposort(data):
         try:
             func = function_def_to_graph(fdef, input_shapes=input_shapes)
         except:  # pylint: disable=bare-except
-            # if there is a missmatch between caller and function use the functions shape
-            logger.warning("shape missmatch between caller and function: %s", k)
+            # if there is a mismatch between caller and function use the functions shape
+            logger.warning("shape mismatch between caller and function: %s", k)
             func = function_def_to_graph(fdef)
         _FUNCTIONS[k] = func
         _, _, _, _, _, tfunctions = tflist_to_onnx(func, {})