  The classical division algorithm for polynomials requires $O(n^2)$ operations
for inputs of size $n$. Using reversal technique and Newton iteration, it can
be improved to $O({M}(n))$, where ${M}$ is a multiplication time. But the
method requires that the degree of the modulo, $x^l$, should be the power of 2.
If $l$ is not a power of 2 and $f(0)=1$, Gathen and Gerhard suggest to compute
the inverse,$f^{-1}$, modulo $x^{\lceil l/2^r\rceil}, x^{\lceil
l/2^{r-1}\rceil},..., x^{\lceil l/2\rceil}, x^l$, separately. But they did not
specify the iterative step. In this note, we show that the original Newton
iteration formula can be directly used to compute $f^{-1}\,{mod}\,x^{l}$
without any additional cost, when $l$ is not a power of 2.
