The transfer-matrix method is used to derive the characteristic equation for electron energy eigenvalues in a generalized infinite one-dimensional binary alloy. The alloy is divided into unit cells and subcells so that the method used is independent of the shape of the potential barriers. Application of the technique to a type-AB one-dimensional alloy represented by an infinite chain of two kinds of square potential barriers gives the energy eigenvalue equation for this case explicitly and for the first time. The formalism is also shown to give the Kronig-Penney result for a chain of identical square potentials.