  In this paper, we present an algorithm of simple exponential growth called
COPOMATRIX for determining the copositivity of a real symmetric matrix. The
core of this algorithm is a decomposition theorem, which is used to deal with
simplicial subdivision of $\hat{T}^{-}=\{y\in \Delta_{m}| \beta^Ty\leq 0\}$ on
the standard simplex $\Delta_m$, where each component of the vector $\beta$ is
-1, 0 or 1.
