-should be buffer name in the sequence to be tried. That name will be
-considered acceptable, if it is tried, even if a buffer with that name
-exists.
+should be a string; it makes a difference if it is a name in the
+sequence of names to be tried. That name will be considered acceptable,
+if it is tried, even if a buffer with that name exists. Thus, if
+buffers named @samp{foo}, @samp{foo<2>}, @samp{foo<3>} and @samp{foo<4>}
+exist,
+
+@example
+(generate-new-buffer-name "foo")
+ @result{} "foo<5>"
+(generate-new-buffer-name "foo" "foo<3>")
+ @result{} "foo<3>"
+(generate-new-buffer-name "foo" "foo<6>")
+ @result{} "foo<5>"
+@end example