Is there a better way to store a twoway dictionary than storing its inverse separate?

Given a one-to-one dictionary (=bijection) generated à la

for key, value in someGenerator:
     myDict[key] = value

an inverse lookup dictionary can be trivially created by adding

    invDict[value] = key

to the for loop. But is this a Pythonic way? Should I instead write a class Bijection(dict) which manages this inverted dictionary in addition and provides a second lookup function? Or does such a structure (or a similar one) already exist?