On-lattice protein structure prediction with empirical energy minimisation has drawn significant research effort. However, energy minimisation with free-modelling not necessarily leads to structures that are similar to the native structure of the given protein. In this paper, we show that energy minimisation has a positive correlation with structural similarity measures if we consider secondary motifs. We then present a constraint-based evolutionary local search framework for on-lattice protein structure prediction using secondary structural information. We approximate secondary motifs such as a-helix and ߭strands on the lattice and propose a set of neighbourhood generation operators that respect those motifs. Our experimental results show significant improvement over the state-of-the-art methods in terms of similarity with the native structures determined by laboratory methods.