Summary: ``In this paper, a branch-and-bound algorithm for finding all cliques of size $k$ in a $k$-partite graph is proposed that improves upon the method of T. Grünert et al. [Comput. Oper. Res. {\bf 29} (2002), no.~1, 13--31; MR1860472 (2002g:90084)]. The new algorithm uses bit-vectors, or bitsets, as the main data structure in bit-parallel operations. Bitsets enable a new form of data representation that improves branching and backtracking of the branch-and-bound procedure. Numerical studies on randomly generated instances of $k$-partite graphs demonstrate competitiveness of the developed method.''