A symmetric tensor is called copositive if it generates a multivariate form taking nonnegative values over the nonnegative orthant. Copositivity of tensors plays an im-portant role in polynomial optimization, tensor complementarity problem and tensor generalized eigenvalue complementarity problem. In this report, we consider an alter-native form of a previously given algorithm for copositivity of high order tensors and its applications in hypergraph. For this purpose, we first give several new conditions for copositivity of tensors based on the representative matrix of a simplex. Then a new algorithm is proposed with the help of a proper convex subcone of the copositive tensor cone. Furthermore, with the help of a sum-of-squares program problem, we define two new subset of copositive tensor cone and discuss their convexity. As an application of the proposed algorithms, we can compute an upper bound for the coclique number of a uniform hypergraph. At last, all kinds of numerical examples are given to show the performance of the algorithms.