This is a theoretical study of a situation where each residue of a linear biopolymer may adopt one of three conformational states. Such a situation exists in the case of DNA, since it may be in helical A, B, . . ., Z forms as well as the melted state. In the vicinity of the triple point in the phrase diagram three states, e.g. the A form, the B form and the denatured state, co-exist within a given molecule. We present an exact analytical solution of the simplest homopolymer model. Theory predicts that the presence of two helical states in one molecule should affect the helix-coil transition in two ways. The melting temperature experiences an upward shift and the melting range width is increased, by a factor of square root of two as a maximum.