We give a formulation, via (1, - 1) matrices, of Mathon's construction for conference matrices and derive a new family of conference matrices of order 5·9²r+1 + 1, t ≥ 0. This family produces a new conference matrix of order 3646 and a new Hadamard matrix of order 7292. In addition we construct new families of Hadamard matrices of orders 6.9²r+1+ 2, 10.9²t+1 + 2, 8·49·9², t ≥ 0; q2(q + 3) + 2 where q ≡ 3 (mod 4) is a prime power and 1/2(q + 5) is the order of a skew-Hadamard matrix); (q + 1)q².9t, t ≥ o (where q ≡ 7 (mod 8)is a prime power and 1/2(q + 1) is the order of an Hadamard matrix). We also give new constructions for Hadamard matrices of order 4·9' ≥ 0 and (q + l)q² (where q ≡ 3 (mod 4) is a prime power).