In this paper we prove that if there are strongly disjoint T-matrices of order t and suitable T-matrices of order t', there are T-matrices of order tt'. We also show that there exist strongly disjoint T-matrices of order t = 73, 79, 113 and (2m+p), p odd, where m+p, m+p, m, m are lengths of base sequences, and give some new constructions of suitable T-matrices of order t = 9, 13, 17, 19, 21, 25. This generalizes the work of...