New constructions for amicable orthogonal designs are given. These new designs then give new amicable Hadamard matrices and new skew-Hadamard matrices. In particular we show that if p is the order of normalized amicable Hadamard matrices there are normalized amicable Hadamard matrices of order (p - 1)u + 1, u > 0 an odd integer.
Tables are given for the existence of amicable and skew-Hadamard matrices of orders 2tq, t ≥ 2 an integer, q(odd)≤2000. This gives further evidence to support the conjecture that "for every odd integer q there exists an integer t (dependent on q) so that there is a skew-Hadamard matrix of order 2tq."