  We study the stability of the SYK$_4$ model with a large but finite number of
fermions $N$ with respect to a perturbation, quadratic in fermionic operators.
We develop analytic perturbation theory in the amplitude of the SYK$_2$
perturbation and demonstrate the stability of the SYK$_4$ infra-red asymptotic
behavior characterized by a Green function $G(\tau) \propto 1/\tau^{3/2} $,
with respect to weak perturbation. This result is supported by exact numerical
diagonalization. Our results open the way to build a theory of non-Fermi-liquid
states of strongly interacting fermions.
