In this work we propose a new distance measure for compar-ing two protein structures based on their contact map representations. We show that our novel measure, which we refer to as the maximum con-tact map overlap (max-CMO) metric, satisfies all properties of a metric on the space of protein representations. Having a metric in that space allows to avoid pairwise comparisons on the entire database and thus to significantly accelerate exploring the protein space compared to non-metric spaces. We show on a gold-standard classification benchmark set of 6, 759 and 67, 609 proteins, resp., that our exact k-nearest neighbor scheme classifies up to 95% and 99% of queries correctly. Our k-NN classification thus provides a promising approach for the automatic clas-sification of protein structures based on contact map overlap.