diff --git a/src/eval.c b/src/eval.c
index 4d45ae2..fa9966e 100644
--- a/src/eval.c
+++ b/src/eval.c
@@ -18259,11 +18259,21 @@
     rettv->v_type = VAR_STRING;
 #ifdef FEAT_PERSISTENT_UNDO
     {
-	char_u *ffname = FullName_save(get_tv_string(&argvars[0]), FALSE);
+	char_u *fname = get_tv_string(&argvars[0]);
 
-	if (ffname != NULL)
-	    rettv->vval.v_string = u_get_undo_file_name(ffname, FALSE);
-	vim_free(ffname);
+	if (*fname == NUL)
+	{
+	    /* If there is no file name there will be no undo file. */
+	    rettv->vval.v_string = NULL;
+	}
+	else
+	{
+	    char_u *ffname = FullName_save(fname, FALSE);
+
+	    if (ffname != NULL)
+		rettv->vval.v_string = u_get_undo_file_name(ffname, FALSE);
+	    vim_free(ffname);
+	}
     }
 #else
     rettv->vval.v_string = NULL;
diff --git a/src/version.c b/src/version.c
index b2f9a98..ce22d9f 100644
--- a/src/version.c
+++ b/src/version.c
@@ -715,6 +715,8 @@
 static int included_patches[] =
 {   /* Add new patch number below this line */
 /**/
+    512,
+/**/
     511,
 /**/
     510,