An algorithm is given for computing the inverse of a multiblock circulant matrix. The algorithm uses only complex variables, roots of unity and normal matrix/vector operations. Procedures for inverting a circulant matrix are reviewed and applied to a multiblock case. A routine BLKCIRC described in an algorithmic form which produces a new sequence of vectors from a given set. This is then utilized for computing the inverse. The overhead for calling BLKCIRC and problems of ill-conditioning are ignored.