  Let $\phi_H^r(n)$ be the smallest integer such that, for all $r$-graphs $G$
on $n$ vertices, the edge set $E(G)$ can be partitioned into at most
$\phi_H^r(n)$ parts, of which every part either is a single edge or forms an
$r$-graph isomorphic to $H$. The function $\phi^2_H(n)$ has been well studied
in literature, but for the case $r\ge 3$, the problem that determining the
value of $\phi_H^r(n)$ is widely open. Sousa (2010) gave an asymptotic value of
$\phi_H^r(n)$ when $H$ is an $r$-graph with exactly 2 edges, and determined the
exact value of $\phi_H^r(n)$ in some special cases. In this paper, we first
give the exact value of $\phi_H^r(n)$ when $H$ is an $r$-graph with exactly 2
edges, which improves Sousa's result. Second we determine the exact value of
$\phi_H^r(n)$ when $H$ is an $r$-graph consisting of exactly $k$ independent
edges.
