The achromatic index of a graph \(G\) is the maximum integer \(k\) such that there exists a proper colouring of the edges (i.e. in which no two adjacent edges have the same colour) in which each pair of colours appear on some pair of adjacent edges. The achromatic index of the complete graph \(K_n\) with \(n\) vertices is denoted by \(A(n)\). It is proved that \(A(12)=32\).