Schrödinger equation in one dimension is assumed solvable by the shooting method.
The first tentative "shot" (initiated in the origin) "misses" the asymptotic boundary conditions of course.
Our proposal: The "Newton's" wavefunction corrections are evaluated simultaneously.
The quadratic rate of convergence of energies is achieved.
Numerical (anharmonic oscillator) tests added.
Published in Phys. Lett. A 230 (1997) 283 - 287.