  We give a new completion for the quasi-uniform spaces. We call the whole
procedure {\it $\tau$-completion} and the new space {\it $\tau$-complement of
the given}. The basic result is that every $T_{_0}$ quasi-uniform space has a
$\tau$-completion. The $\tau$-complement has some \textquotedblleft
crucial\textquotedblright properties, for instance, it coincides with the
classical one in the case of uniform space or it extends the {\it Doitcinov's
completion for the quiet spaces}. We use nets and from one point of view the
technique of the construction may be considered as a combination of the {\it
Mac Neille's cut} and of the completion of partially ordered sets via {\it
directed subsets}.
