Abstract
It is known that the construction of a completely stable solution in Horndeski theory is restricted very strongly by the so-called no-go theorem. Previously, various techniques have been used to avoid the conditions of the theorem. In this paper a new way of constructing stable solutions are shown in the general Horndeski theory. We considered the situation in which the unitary gauge studied earlier turns out to be singular. On this basis we construct a spatially flat, stable bouncing and genesis Universe solutions which are described by General Relativity with non-conventional scalar field.