  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.
