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 contact 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 no-metric spaces. We show on a small gold-standard superfamily classification benchmark set of 6, 759 proteins that our exact scheme classifies up to 224 out of 236 queries correctly and on an larger, extended version of the benchmark up to 1361 out of 1369 queries. Our k-NN classification thus provides a promising approach for the automatic classification of protein structures into SCOP or CATH based on flexible contact map overlap alignments.