[Haskell-beginners] How to select items from one list depending on another

[C K Kashyap]

Hi,
I have this problem at hand -

Given two lists

list1 = [0,1,2,0,1,4]

list2 = [1,2,3,4,5,6]

I need to take items from the second list only when the corresponding
item in list1 is non-zero.

list3 = map snd $ filter takeValid $ zip list1 list2 where
                       takeValid (a,b) = a /= 0

Is there a shorter way?


-- 
Regards,
Kashyap