A symmetric matrix is called copositive if it generates a quadratic form taking no negative values over the positive orthant, and the linear optimization problem over the set of copositive matrices is called the copositive programming problem. Recently, many studies have been done on the copositive programming problem (cf, Dur (2010)). Among others, several branch and bound type algorithms have been provided to test copositivity since it is known that the problem for deciding whether a given matrix is copositive is co-NP-complete (cf. Murty and Kabadi (1987)). In this talk, we propose a new branch and bound type algorithm for this testing problem. Our algorithm is based on solving linear optimization problems over the nonnegative orthant, repeatedly. Numerical experiments suggest that our algorithm is promising for determining upper bounds of the maximum clique problem.