diff --git a/Doc/c-api/module.rst b/Doc/c-api/module.rst
index 230b471d473be7..bc5fa32ac5acec 100644
--- a/Doc/c-api/module.rst
+++ b/Doc/c-api/module.rst
@@ -449,10 +449,11 @@ state:
    Add an object to *module* as *name*.  This is a convenience function which
    can be used from the module's initialization function.
 
-   On success, return ``0``. On error, raise an exception and return ``-1``.
+   On success, return ``0``.
 
-   Return ``NULL`` if *value* is ``NULL``. It must be called with an exception
-   raised in this case.
+   If *value* is ``NULL`` (indicating failure), raise an exception and return
+   ``-1``.  If an exception is set, raise that exception.  If no exception is
+   set, raise :exc:`SystemError`.
 
    Example usage::