Recursive mutex locks

This is how I want it to work:

Thread A, locks mutex Q.
Thread A then hands over the mutex to thread B.
Thread B does some processing.
In Thread A tries to lock mutex Q again, blocks waiting for the mutex to become
available. (*)
Thread B does some more processing.
Thread B releases mutex Q.
Thread A starts over at the top (and locks mutex Q).

This (obviously) doesn't work, because at point (*) I get an error
back saying: "Recursive mutex locks!"

Well, I understand what it is complaining about, but how do I "donate"
a mutex to another thread?  Or is there a way to tell the mutex library
to ignore the fact that it's the same thread that tries to lock it?
-- 
Stephen.