  Let $G$ be a finite group. We will say that $M$ and $S$ form a
\textsl{complete splitting} (\textsl{splitting}) of $G$ if every element
(nonzero element) $g$ of $G$ has a unique representation of the form $g=ms$
with $m\in M$ and $s\in S$, and $0$ has a such representation (while $0$ has no
such representation). In this paper, we determine the structures of complete
splittings of finite abelian groups. In particular, for complete splittings of
cyclic groups our description is more specific. Furthermore, we show some
results for existence and nonexistence of complete splittings of cyclic groups
and find a relationship between complete splittings and splittings for finite
groups.
