Generate a random index from list which does not include one specific index

I have a list of integers: l = [1,2,3,4]

For each element in this list I need to randomly select a different element and perform some operation on it:

for i in range(len(l)):
   idx = # a random index which is NOT equal to i
   # do something with the element at idx

I'm still pretty new to Python and can't determine if there is a way to do this without resorting to a loop where I generate a random index and only stop the loop if the random number is not equal to i. Any suggestions would be greatly appreciated.