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

A solution to the completion problem of quasi-uniform spaces