diff --git a/Doc/library/hashlib.rst b/Doc/library/hashlib.rst
index 4f5aac9080d..f0fe915ce5e 100644
--- a/Doc/library/hashlib.rst
+++ b/Doc/library/hashlib.rst
@@ -40,12 +40,12 @@ concatenation of the data fed to it so far using the :meth:`digest` or
 
 .. note::
 
-   For better multithreading performance, the Python GIL is released for
+   For better multithreading performance, the Python :term:`GIL` is released for
    strings of more than 2047 bytes at object creation or on update.
 
 .. note::
 
-   Feeding string objects is to :meth:`update` is not supported, as hashes work
+   Feeding string objects into :meth:`update` is not supported, as hashes work
    on bytes, not on characters.
 
 .. index:: single: OpenSSL; (use in module hashlib)