  In this paper we describe the thickened strips and the outside nested
decompositions of any skew shape $\lambda/\mu$. For any such decomposition
$\Phi=(\Theta_1,\Theta_2,\ldots,\Theta_g)$ of the skew shape $\lambda/\mu$
where $\Theta_i$ is a thickened strip for every $i$, if $r$ is the number of
boxes that are contained in any two distinct thickened strips of $\Phi$, we
establish a determinantal formula of the function
$s_{\lambda/\mu}(X)p_{1^r}(X)$ with the Schur functions of thickened strips as
entries, where $s_{\lambda/\mu}(X)$ is the Schur function of the skew shape
$\lambda/\mu$ and $p_{1^r}(X)$ is the power sum symmetric function index by the
partition $(1^r)$. This generalizes Hamel and Goulden's theorem on the outside
decompositions of the skew shape $\lambda/\mu$. As an application of our
theorem, we derive the number of $m$-strip tableaux which was first counted by
Baryshnikov and Romik via extending the transfer operator approach due to
Elkies.
