Summary: Univariate conditioning of copulas is studied, yielding a construction method for copulas based on an a priori given copula. Based on the gluing method, the \(g\)-ordinal sum of copulas is introduced and a representation of copulas by means of \(g\)-ordinal sums is given. Though different right conditionings commute, this is not the case of right and left conditioning, with a special exception of Archimedean copulas. Several interesting examples are given. Especially, any Ali-Mikhail-Haq copula with a given parameter \(\lambda > 0\) allows to construct via conditioning any Ali-Mikhail-Haq copula with parameter \(\mu \in [0,\lambda ]\).