A binary matrix has the Consecutive Ones Property (C1P) if its columns can be ordered in such a way that all 1s on each row are consecutive. Algorithmic issues of the C1P are central in computa- tional molecular biology, in particular for physical mapping and ances- tral genome reconstruction. In 1972, Tucker gave a characterization of matrices that have the C1P by a set of forbidden submatrices, and a substantial amount of research has been devoted to the problem of ef- ciently nding such a minimum size forbidden submatrix. This paper presents a new O( 3m2 (m + n 3 )) time algorithm for this particular task for a m n binary matrix with at most 1-entries per row, thereby improving the O( 3m2 (mn + n 3 )) time algorithm of Dom et al. [17].