  We establish a nice orthonormal frame field on a closed surface minimally
immersed in a unit sphere $S^{n}$, under which the shape operators take very
simple forms. Using this frame field, we obtain an interesting property
$K+K^{N}=1$ for the Gauss curvature $K$ and the normal curvature $K^{N}$ if the
Gauss curvature is positive. Moreover, using this property we obtain the
pinching on the intrinsic curvature and normal curvature, the pinching on the
normal curvature, respectively.
