diff --git a/doc/design/backward.md b/doc/design/backward.md
index 35f03692bb052e0a04db18d28f6f8d901215a553..20fda7a98f514a3f1c1c2d0ba7447ec954b21d5a 100644
--- a/doc/design/backward.md
+++ b/doc/design/backward.md
@@ -106,9 +106,11 @@ See function `_addup_repetitive_outputs_` in `backward.py` for implementation de
 
 In our framework, variables can be marked as *no_gradient*, it means that the gradient of this variable is unnecessary and can be considered as zero in model training. Apparently, when all the outputs of some `grad_op` are marked as *no_gradient*, the `grad_op` itself can be skipped in backward pass. 
 
-But these unnecessary gradients still need to be creating and initialized by something, otherwise following `grad_op`s who take these gradients as inputs take the risk of using uninitialized memory. In our code, we employ `fill_zeros_like_op` to initialize them as all zeros. 
+Another situation is all the gradient inputs of some `grad_op` are marked as *no_gradient*, which means all of them can be considered as zeros. For `grad_op`s are in essence the propagation of gradients, all the outputs are definitely zeros when all gradient inputs are zeros. Therefore the `grad_op` can also be skipped.
 
-This features are implemented in function `_remove_no_grad_branch_`. It checks new created `grad_op`s one-by-one, removes whose outputs are all in `no_grad_set` or inserts `fill_zeros_like_op` when its necessary. We can get the `no_grad_set` from the `_append_backward_ops_` argument `no_grad_dict` or generate it on the fly by scanning all variables' `no_gradient` attribute(True or False). 
+It should be noted that all these zero gradients still need to be creating and initialized by something, otherwise following `grad_op`s who take these gradients as inputs take the risk of using uninitialized memory. In our code, we employ `fill_zeros_like_op` to initialize them as all zeros. 
+
+This features are implemented in function `_remove_no_grad_branch_`. It checks new created `grad_op`s one-by-one, removes who can be skipped and inserts `fill_zeros_like_op` when its necessary. We can get the `no_grad_set` from the `_append_backward_ops_` argument `no_grad_dict` or generate it on the fly by scanning all variables' `no_gradient` attribute(True or False). 
 
 ### Creating Backward Variables
 
diff --git a/python/paddle/v2/fluid/backward.py b/python/paddle/v2/fluid/backward.py
index 43e9abc354d8e03add2b1a25acf531e6d1d0b1a7..a1be768daa2dfa20f0c3b71f429581e9ca2932b5 100644
--- a/python/paddle/v2/fluid/backward.py
+++ b/python/paddle/v2/fluid/backward.py
@@ -138,7 +138,7 @@ def _remove_no_grad_branch_(op_descs, no_grad_set):
     Remove unnecessary grad ops
     A grad op can be removed in two cases:
         1. all outputs of the grad op are in 'no_grad_set'
-        2. (TODO) all grad inputs of the grad op are in 'no_grad_set'
+        2. all grad inputs of the grad op are in 'no_grad_set'
     """
 
     def _op_can_be_removed_(op_desc, no_grad_set):