We obtain an expansion of Taylor style of the distribution $\sigma^{(k)}(u(x_1,\dots,x_n)-t)$ where $u(x_1,\dots,x_n)\in C^\infty(R^n)$ without critical points and $t$ is a real number. In particular, we obtain the expansion of the distribution $\sigma^{(k)}(P+m^2)$(see [3-5]), where $m$ is a positive real number and $P=P(x)= x_1^2+ x_2^2+\dots+x_p^2-x^2_{p+1}-\dots-x^2_{p+q}$, $p+q=n$ dimension of the space.