Recently Nandi etc. have proposed a 1/3-rate and a 2/3-rate double length compression functions and studied their security in the black-box model. They proved that to find a collision for the compression function, it requires Ω(2^(2n/3)) queries, where n is the length of output size. In this paper, we show that not all hash functions based on block cipher constructed according to their model are of the same security .i.e., the complexity to find the collisions for these hash functions can be reduced to O(2^(n/2)).