She appeared in the episode "Madame and Her Special Friend" as a rich woman, neighbor of Charlie that was always wrong with him. She dated Alan because one of Charlie's girlfriends with its auto lock the output of her park and she had to go to an appointment with the hairdresser. Alan offers to take her and they go on a couple of dates. Norma proposed to open a clinic with his name and that for a change, could have sex. Alan wanted to say no, but allowed himself to be duped by a Rolex watch that she gifted. Finally he was left without the building because while there were "doing" it, Norma had a cardiac arrest and died. Alan confessed that her last words were "give me back my clock".