We study the collapse transition of a polymer on a square lattice with both nearest-neighbor and next
nearest-neighbor interactions, by calculating the exact partition function zeros up to chain length
36. The transition behavior is much more pronounced than that of the model with nearest-neighbor
interactions only. The crossover exponent and the transition temperature are estimated from the scaling
behavior of the first zeros with increasing chain length. The results suggest that the model is of
the same universality class as the usual еш point described by the model with only nearest-neighbor
interaction.