unexport not working?

[Jay Foad]

unexport doesn't seem to work for me:

$ cat A
unexport FOO
all:
        $(MAKE) -f B
$ cat B
all:
        echo $(FOO)
$ make --no-print-directory -f A FOO=hello
make -f B
echo hello
hello
$

As I understand it, the "unexport" in A should prevent FOO from being
exported to B, so $(FOO) in B should expand to the empty string.

Am I doing something wrong, or is this a bug in make? I'm using:

$ make -v
GNU Make 3.81
Copyright (C) 2006  Free Software Foundation, Inc.
This is free software; see the source for copying conditions.
There is NO warranty; not even for MERCHANTABILITY or FITNESS FOR A
PARTICULAR PURPOSE.

This program built for i486-pc-linux-gnu

... on Debian lenny.

Thanks,
Jay.