In this paper we consider equations arising 
from an optimization problem by the Lagragian method 
and show a new algorithm for solving the equations 
by a generalized Newton method. 
 In a finite number of iterations we can find matrices 
which are closed to the inverse of the Jacobian matrix 
by the generalied Newton method. Moreover we get the 
superlinear convergence to the optimal solution of 
the optimization problem from our theorem.