We develop a new algebraic technique that gives a simple randomized algorithm for the simple k-path problem with the same complexity O(1657k) as in [A. Bj\"orklund. Determinant Sums for Undirected Hamiltonicity. FOCS 2010, pp. 173--182, (2010). A. Bj\"orklund, T. Husfeldt, P. Kaski, M. Koivisto. Narrow sieves for parameterized paths and packings. {\it arXiv}:1007.1161v1, (2010).]