Abstract: The termination of a class of non-linear loop program can be determined.The category of the program termination assignment matrix with positive eigenvalues related to the corresponding feature vector.Then proposed a new method to determine the type of program termination,the method is closely related with the initial assignment of loop iterations and variables.By this method,not only able to determine whether to terminate this category program,but also on not all the initial values are the termination procedures,given recommendations enables the initial value of the program terminates.