Singular solutions of conformal Hessian equation

We show that for any $ϵ\in ]0,1[$ there exists an analytic outside zero solution to a uniformly elliptic conformal Hessian equation in a ball $B\subset {\mathbb{R}}^5$ which belongs to $C^{1,\epsilon} (B)\setminus C^{1,\epsilon+} (B)$.