Graph representations are widely used for dealing with structural information. There are applications, for example, in pattern recognition, machine learning and information retrieval, where one needs to measure the similarity of objects. When graphs are used for the representation of structured objects, then measuring the similarity of objects becomes equivalent to determining the similarity of graphs. The measurement of similarity is normally performed by determining the maximum common subgraph of the graphs in question. This paper presents a new algorithm for determining the maximum common subgraph of a pair of graphs which offers better performance than existing algorithms.