**Let an unperturbed Hamiltonian T possess a tridiagonal matrix form.****Make a trick: Choose any E_0 and "correct" H_0 = T + U with an "ad hoc" separable U.****Gains:****Wavefunctions become easily defined (by recurrences) in any order (incl. zero),**

**the current "unperturbed" diagonalization of H_0 not necessary,**

**replaced by the (much simpler) inversion of T,****using, say, continued fractions.****A modified textbook Rayleigh-Schrödinger perturbation recipe obtained,**

**published in:****Phys. Lett. A 120 (1987) 317 - 321,****Phys. Rev. A 35 (1987) 2448.****etc.**