The paper is dealt with Numerov’s method for solving two-point boundary value problems. As is well-known, the nature of the solution of a continuous problem is not identical with the solution of its discrete analogs. The author presents necessary and sufficient conditions for the existence and uniqueness of the solutions in Numerov’s method, most of them are best possible. From this point of view these conditions are very important. Moreover, the results obtained by the author give an explicit upper bound of the step size in Numerov’s method. The importance of author’s results is confirmed by well-choosen examples.