Stop SIGALRM when function returns

I have a problem that I can't seem to solve by myself. I'm writing a small python script and I would like to know why my signal.alarm still works after the function it's located in returned. Here is the code:

class AlarmException(Exception):
    pass

def alarmHandler(signum, frame):
    raise AlarmException

def startGame():
    import signal
    signal.signal(signal.SIGALRM, alarmHandler)
    signal.alarm(5)
    try:
        # some code...
        return 1
    except AlarmException:
        # some code...
        return -1

def main():
    printHeader()
    keepPlaying = True
    while keepPlaying:
        score = 0
        for level in range(1):
            score += startGame()
        answer = raw_input('Would you like to keep playing ? (Y/N)\n')
        keepPlaying = answer in ('Y', 'y')

So the problem is that when my startGame() function returns, the SIGALRM is still counting down and shutdown my program. Here is the traceback:

Would you like to keep playing ? (Y/N)
Traceback (most recent call last):
  File "game.py", line 84, in <module>
    main()
  File "game.py", line 80, in main
    answer = raw_input('Would you like to keep playing ? (Y/N)\n')
  File "game.py", line 7, in alarmHandler
    raise AlarmException
__main__.AlarmException

How can I proceed to say to SIGALRM to stop when the function it is in has exited ?

Thanks !