This paper introduces an algorithm for sparse approximation in redundant dictionaries, called the M-Term Pursuit (MTP), based on the matching pursuit approach (MP). This algorithm decomposes the signal into a linear combination of selected atoms, chosen to represent the signal components. The MTP algorithm provides adaptive representation for signals in any dictionary. The basic idea behind the MTP, is to partition the dictionary into $L$ disjoint sub-dictionaries, each carrying some meaningful information. Then it iteratively finds a $k$-term approximation. During each iteration, $M$ atoms, where $M