we study the holomorphic embedding problem from a compact real algebraic hypersurface into a sphere. by our theorem, for any integer $n$, there is a family of compact real algebraic strongly pseudoconvex hypersurfaces in $c^2$ , none of which can be locally holomorphically embedded into the unit sphere in $c^n$. this shows that the whitney (or remmert) type embedding theorem in differential topology(or in the stein space theory, respectively) does not hold in the setting above. this is a joint work with xiaojun huang and xiaoshan li.