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Copula models have become popular in different applications, includingmodeling shocks, in view of their ability to describe better the dependenceconcepts in stochastic systems. The class of maxmin copulas was recentlyintroduced by Omladi\v{c} and Ru\v{z}i\'{c}. It extends the well known classesof Marshall-Olkin and Marshall copulas by allowing the external shocks to havedifferent effects on the two components of the system. By a reflection (flip)in one of the variables we introduce a new class of bivariate copulas calledreflected maxmin (RMM) copulas. We explore their properties and show thatsymmetric RMM copulas relate to general RMM copulas similarly as do semilinearcopulas relate to Marshall copulas. We transfer that relation also to maxmincopulas. We also characterize possible diagonal functions of symmetric RMMcopulas.

Reflected maxmin copulas and modelling quadrant subindependence