Koplienko [11] found a trace formula for perturbations of self-adjoint operators by Hilbert-Schmidt class B2(H). Later in 1988, similar was obtained Neidhardt [19] the case unitary operators. In this article, we give still another proof Koplienko-Neidhardt reducing problem to finite dimensional one as Krein's Voiculescu [35], Sinha and Mohapatra [30], [31].