TMZ has obtained the letter that Francis has sent to Madonna and her "co-conspirators." Francis' lawyer threatens to sue all of them for attempting to get a "free ride on the valuable consumer goodwill and brand recognition" of Joe's famous trademark.

Francis' lawyer makes it clear: "Your misappropriation of my clients' trademark will not be tolerated."

But Francis is willing to cut a deal with Madonna, provided she agrees to the following terms:

-- Negotiate an immediate licensing agreement for the use of Joe's trademark
-- Account for the number of time Madonna has already used the trademark
-- NOT PERFORM THE SONG AT THE SUPER BOWL