  Investigating for interior regularity of viscosity solutions to the fully
nonlinear elliptic equation $$F(x,u,\triangledown u,\triangledown ^2 u)=0,$$ we
establish the interior $C^{1+1}$ continuity under the assumptions that $F$ is
uniformly elliptic, H$\ddot o$lder continuous and satisfies the natural
structure conditions of fractional order, but without the concavity assumption
of $F$. These assumptions are weaker and the result is stronger than that of
Caffarelli and Wang[1], Chen[2].
