The problem addressed in this paper is the estimation of the channel parameters in a Code Division Multiple Access(CDMA) communication system, in the presence of multipath effects. Maximum likelihood estimation of these parameters has been investigated in the past with the main drawback being the complexity of the multi-dimensional algorithms. The algorithm presented in this paper elegantly decomposes the multiuser problem into a series of single user problems. The algorithm first estimates a composite channel impulse response of each user and then extracts the channel parameters of all the paths of each user from the channel impulse response. We evaluate the performance of the algorithm through simulation studies.