Аннотация:In the theory of pseudorepresentations, there isan old unsolved problem: whether or not every unbounded pseudorepresentation ofan amenable group with sufficiently small defect admits a close ordinaryrepresentation of the group (and the correction is small together with thedefect). Till now, only partial results of this kind are known in this area. Inthis note, we improve one of the known partial results in this direction.