New results are presented for the prediction of secondary structure information for protein sequences using Hidden Markov Models (HMMs) evolved using a Genetic Algorithm (GA). We achieved a Q3 measure of 75% using one of the most stringent data set ever used for protein secondary structure prediction. Our results beat the best hand-designed HMM currently available and are comparable to the best known techniques for this problem. A hybrid GA incorporating the Baum-Welch algorithm was used. The topology of the HMM was restricted to biologically meaningful building blocks. Mutation and crossover operators were designed to explore this space of topologies.