We present a method for calculating the electronic structure of disordered alloys with shortrange order (SRO) which guarantees a positive density of states for all values of the SRO parameter. The method is based on the generalized augmented-space theorem which is valid for alloys with SRO. This theorem is applied to alloys with SRO in the tight-binding linear-muffin-tin-orbital (TB-LMTO) framework. This is done by using the augmented-space formulation of Mookerjee and the cluster-coherent-potential approximation. As an illustration, the method is applied to a single-band model TB-LMTO Hamiltonian. We find that the SRO can induce substantial changes in the density of states