Antidictionaries are in particular useful for source coding. In one dimension, for an input string, there are fast construction algorithms of an antidictionary in which a suffix tree that stores all the substrings of the string is utilized. However, in two dimension (2D), for an n×n input square or rectangle, there is no fast construction algorithm of an antidictionary except a straight-forward algorithm in O(n8) time. In this paper, we propose a 2D suffix trie which stores all the subrectangles of an input rectangle and present an algorithm to construct a 2D suffix trie in O(n4 log n) time. A 2D suffix trie consists of two suffix tries with suffix links rowwise and columnwise. Moreover, we propose a fast construction algorithm of a two-dimensional antidictionary using a 2D suffix trie in O(n5 log n) time, and their effectivenesses are demonstrated by simulation results.