Аннотация:A new method is proposed for estimating the error in the numerical solution of a second-order differential equation by the Störmer method. With the use of the difference equation, for the error at each step, along with the calculation of the numerical solution an ellipsoid is constructed containing the error of this numerical solution. This method can also be applied to systems of second-order differential equations. Examples demonstrating its applicability to the cases where the coordinatewise estimates are too crude are presented.