In this paper, by the use of Latin squares, we describe a procedure to construct Hadamard matrices using the existing Hadamard matrices of order m as input matrices. We propose constructions of Hadamard matrices of orders m(m − 1), m(m 2 − 1) and m(m k − 1), where k is a multiple of four that divides m into an even number. This work is a continuation of our previous one in [5].