It is shown both analytically and numerically for a number of examples that both radial and rotational nonadiabatic couplings within the standard adiabatic approach depend on the origin of the light-particle coordinates and the ambiguity in the nonadiabatic couplings does not lead to ambiguity in the coupled channel equations. The examples considered are the nH, nD, npmu(-) quasimolecules, for which the nonadiabatic couplings can be calculated analytically, and the HeH molecule, for which ab initio calculations are carried out. Analytical formulas for couplings calculated with the shifted origin are derived. The coupled equations take their simplest form in Jacobi coordinates for which many nonadiabatic couplings are nonzero, even for such noninteracting systems as nH, nD, and npmu(-). These couplings are a fundamental feature of the adiabatic approach.