A mobile ad hoc network (MANET) is a decentralized network of mobile nodes. Due to the broadcast nature of radio transmissions, communication in MANETs is more susceptible to malicious traffic analysis. An interesting problem is how to thwart malicious traffic analysis. Most anonymous communication protocols are based on the pseudonyms of mobile nodes. However, conventional pseudonym schemes have some limitations such as collisions of pseudonyms and high computational complexity due to the use of cryptographic hash functions. Collisions of identities are not desirable since they are the main causes for reduced effective bandwidth, increased energy consumption and non-deterministic data delivery. In this paper, we propose a new collision-free pseudonym scheme to enable anonymous communication. In our approach, each node generates pseudonyms by using a permutation matrix without collisions. The challenging issue is how to store the overall permutation matrix. It is practically hard to assume that mobile nodes maintain the permutation matrix due to the limitation of resources. Therefore we design the online computation of each node's own pseudonym without loading the overall matrix.