A ``decoherent'' measurement is a dephasing plus tracing out plus triorthogonal decomposition. Dephasing can happen any time when a small system is coupled with a large reservoir: It is in principle reversible. But in order to have a measurement we also need the tracing out and the triorthogonal decomposition. The first requirement is observation-dependent (because environment plus apparatus plus object system eventually remain in a superposition). But the second one is an irreversible and irrelative change: In the presence of three ``systems'' the basis degeneracy problem disappears, i.e. there can be diagonalization only relatively to an observable (the measured one).