A new polynomial matrix method has been proposed to calculate the energy levels of the π-electrons of a linear conjugated polymer in the framework of the H.M.O. approximation. The polynomial matrix is a 2 × 2 matrix, one element of which is the secular polynomial for the building block, and the rest are obtained by eliminating one or both the atoms through which the building blocks are linked with each other. The secular polynomial for the polymeric molecule then happens to be one element of the polynomial matrix for the entire chain obtained by suitable multiplication of individual polynomial matrices. Linking of the chain through heteroatoms can be taken into account by introducing a k-matrix governed by the resonance integral for this bond. The secular polynomial for the polymer can be arrived at in a simple way provided it contains repetition of identical building units. For an infinite chain polymer, the energy bands are given by a single equation. This method is capable of handling disordered polymers.