Sterile neutrino creating a reduced LSND effect

Although the hypothetic sterile neutrino $\nu_s$ is probably not involved significantly in the deficits of solar $\nu_e$'s and atmospheric $\nu_\mu$'s, it may cause the possible LSND effect. In fact, we face such a situation, when the popular nearly bimaximal texture of active neutrinos $\nu_e$, $\nu_\mu$, $\nu_\tau$ is perturbed through a small rotation in the 14 plane, where $\nu_4$ is the extra neutrino mass state induced by the sterile neutrino $\nu_s$. Then, with $m^2_1\simeq m^2_2$ we predict in the simplest case of $s_{13}\to0$ that $\sin^22\theta_{\rm LSND}=s^4_{14}/2$ and $\Delta m^2_{\rm LSND} = |\Delta m^2_{41}|$. However, the negative CHOOZ experiment imposes on $s^4_{14}/2$ the upper bound $1.3\times10^{-3}$, suggesting a reduction of the amplitude of possible LSND effect.