A zero-suppressed binary decision diagram is a compressed data structure that represents families of sets. There are various basic operations to manipulate families of sets over ZDDs such as union, intersection, and difference. They can be efficiently computed without decompressing ZDDs. Among them, there are many important unary operations such as computing the ZDD for all extremal sets ( maximal sets or minimal sets) from an input ZDD. Unary operations are useful in various fields such as constraint programming, data mining, and artificial intelligence. Therefore, they must be efficiently computed. In this paper, we propose a general framework for parallel unary operations on ZDDs. We analyze the computational complexity and evaluate the effectiveness of our method by performing computational experiments.