A social network-based friend recommendation system should not only be able to reduce computing time complexity, but also to improve the recommendation accuracy. Matchmaking involves comparing the interests of the users with those of their friends on the social networking site to find new friends with similar interests. Match theory is applied in experimental economics to study the match between resources and markets. The interest matching algorithm presented in this paper is a modified version of the Gale-Shapley algorithm. To demonstrate the ability of the algorithm to provide friend recommendations, it was applied using Facebook website data to calculate the best stable match combination. The simulation results show that the proposed approach can be easily and quickly utilized by management to match user interests and friend recommendations.