We study stability of the SYK₄ 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 SYK₂ perturbation and demonstrate stability of the SYK₄
infra-red asymptotic behavior characterized by a Green function G(t) µ 1/t^3/2, with respect to weak  perturbation.  This result is supported by exact numerical diagornalization.  Our results open the way to build a theory of non-Fermi-liquid states of strongly interacting fermions.