The use of Genetic Algorithms in a 2D Hydrophobic-Hydrophilic (HP) model in protein folding prediction application requires frequent fitness function computations. While the fitness computation is linear, the overhead incurred is significant with respect to the protein folding prediction problem. Any reduction in the computational cost will therefore assist in more efficiently searching the enormous solution space for protein folding prediction. This paper proposes a novel pruning strategy that exploits the inherent properties of the HP model and guarantee reduction of the computational complexity during an ordered traversal of the amino acid chain sequences for fitness computation, truncating the sequence by at least one residue.