A powerful CACSD package, based on the design method of Boyd et ah , has been constructed. This method translates the control system design problem into, and solves it as, a linearly constrained quadratic programming problem. The efficiency of the design method, in terms of both memory requirements and execution speed, has been improved substantially. To achieve this, a diagonal factorization technique has been developed; when applied to the left factorization of the plant transfer function matrix, it allows the multivariable design problem of size αN2 to be reduced to N sub-problems each of size αN, which may then be solved independently. Although this diagonal factorization is not always coprime, it is suitable for a wide range of plant transfer function matrices. A theorem to check that the factorization is coprime was developed, and is easy to apply. Formulae for (non-diagonal) coprime factorizations, where the nominal stabilizing controller is stable, have also been presented. A novel parameterization for the design transfer function Q has been introduced; by appropriate choice of the QSTEP parameter the designer benefits from the efficiency of a low order approximation and while often enjoying almost the same precision as for a high order approximation. Finally, a very efficient representation for the linear constraints generated by the design method has been developed.