Аннотация:As is known, for a sufficiently small defect of a (not necessarily bounded) quasirepresentation of an amenable group in a reflexive Banach space E with dense set of bounded orbits, there is an extension of this quasirepresentation for which there is a close ordinary representation of the group in the space of this extension. In the present note it is proved that, if the original quasirepresentation π of an amenable group G in a reflexive Banach space E is a pseudorepresentation, then an ordinary representation of G, in the vector subspace L of E formed by vectors with bounded orbits and equipped with a natural Banach norm, which is close to π|L (this ordinary representation exists if the defect of π is sufficiently small) is equivalent to π|L.