This article deals with a variant of the Nash-Moser implicit function theorem about the solvability of the problem \(\phi(u) = 0\) with a \(C^2\)-operator \(\phi\) mapping an open set \(U_k \subset {\mathcal B}_\infty^k \to B_\infty^k\) for all \(k \geq 0\) where \({\mathcal B}_\infty^k = \bigcap_{s > 0} {\mathcal B}_s^k\), \(B_\infty^k = \bigcap_{s > 0} B_s^k\) and \({\mathcal B}_s^k\), \(B_s^k\) are two families (scales) of Banach spaces with some natural properties. Some (cumbersome and immense) conditions for the solvability of the problem \(\phi(u) = 0\) are formulated. The authors state that their theorem is applicable in the cases when linearized equation have right inverses with error terms of second order or when in each recurrence step it must be solved a linearized equations in Sobolev space with different weights in each weighted Sobolev space (in particular, this latter situation takes place in an embedding problem of a Cauchy-Riemann structure). Concrete examples are absent.