We present MinMax, a new algorithm for mining maximal frequent itemsets(MFI) from a transaction database. It is based on depth-first traversal and iterative. It combines a vertical tidset representation of the database with effective pruning mechanisms. MinMax removes all the non-maximal frequent itemsets to get the exact set of MFI directly, needless to enumerate all the frequent itemsets from smaller ones step by step. It backtracks to the proper ancestor directly, needless level by level. We found MinMax to be more effective than GenMax, a state-of-the-art algorithm for finding maximal frequent itemsets, to prune the search space to get the exact set of MFI.