The variable metric algorithm is a frequently used method for calculating the least value of a function of several variables. However it has been proved only that the method is successful if the objective function is quadratic, although in practice it treats many types of objective functions successfully. This paper extends the theory, for it proves that successful convergence is obtained provided that the objective function has a strictly positive definite second derivative matrix for all values of its variables. Moreover it is shown that the rate of convergence is super-linear.