An Hadamard matrix H is a square matrix of order n all of whose entries are ± 1 such that There are matrices of order 1 and 2 and for all other Hadamard matrices the order n is a multiple of 4, n = 4 m . It is a reasonable conjecture that Hadamard matrices exist for every order which is a multiple of 4 and the lowest order in doubt is 268. With every Hadamard matrix H 4m a symmetric design D exists with