For the analysis of discrete sequences, frequent episode mining (FEM) is a key technique. The goal is to enumerate all subsequences of symbols or events that are appearing at least some minimum number of times. In the last decades, several efficient episode mining algorithms were designed. Nonetheless, a major issue is that they often yield a huge number of frequent episodes, which is inconvenient for users. As a solution, this paper presents an efficient algorithm called MaxFEM (Maximal Frequent Episode Miner) to identify only the maximal frequent episodes of a complex sequence. A major benefit is to reduce the set of frequent episodes presented to the user. MaxFEM includes many strategies to improve its performance. The evaluation of MaxFEM on real datasets confirms that it has excellent performance.