  For any $p\in(0,\,1]$, let $H^{\Phi_p}(\mathbb{R}^n)$ be the Musielak-Orlicz
Hardy space associated with the Musielak-Orlicz growth function $\Phi_p$,
defined by setting, for any $x\in\mathbb{R}^n$ and $t\in[0,\,\infty)$,
  $$ \Phi_{p}(x,\,t):= \begin{cases} \frac{t}{\log(e+t)+[t(1+|x|)^n]^{1-p}} &
\qquad \text{when } n(1/p-1)\notin \mathbb{N} \cup \{0\}; \\
\frac{t}{\log(e+t)+[t(1+|x|)^n]^{1-p}[\log(e+|x|)]^p} & \qquad \text{when }
n(1/p-1)\in \mathbb{N}\cup\{0\},\\ \end{cases} $$ which is the sharp target
space of the bilinear decomposition of the product of the Hardy space
$H^p(\mathbb{R}^n)$ and its dual. Moreover, $H^{\Phi_1}(\mathbb{R}^n)$ is the
prototype appearing in the real-variable theory of general Musielak-Orlicz
Hardy spaces. In this article, the authors find a new structure of the space
$H^{\Phi_p}(\mathbb{R}^n)$ by showing that, for any $p\in(0,\,1]$,
$H^{\Phi_p}(\mathbb{R}^n)=H^{\phi_0}(\mathbb{R}^n) +H_{W_p}^p(\mathbb{R}^n)$
and, for any $p\in(0,\,1)$, $H^{\Phi_p}(\mathbb{R}^n)=H^{1}(\mathbb{R}^n)
+H_{W_p}^p(\mathbb{R}^n)$, where $H^1(\mathbb{R}^n)$ denotes the classical real
Hardy space, $H^{\phi_0}(\mathbb{R}^n)$ the Orlicz-Hardy space associated with
the Orlicz function $\phi_0(t):=t/\log(e+t)$ for any $t\in [0,\infty)$ and
$H_{W_p}^p(\mathbb{R}^n)$ the weighted Hardy space associated with certain
weight function $W_p(x)$ that is comparable to $\Phi_p(x,1)$ for any
$x\in\mathbb{R}^n$. As an application, the authors further establish an
interpolation theorem of quasilinear operators based on this new structure.
