  Koplienko \cite{Ko} found a trace formula for perturbations of self-adjoint
operators by operators of Hilbert-Schmidt class $\mathcal{B}_2(\mathcal{H})$.
Later in 1988, a similar formula was obtained by Neidhardt \cite{NH} in the
case of unitary operators. In this article, we give a still another proof of
Koplienko-Neidhardt trace formula in the case of unitary operators by reducing
the problem to a finite dimensional one as in the proof of Krein's trace
formula by Voiculescu \cite{Voi}, Sinha and Mohapatra \cite{MoSi94,MoSi96}.
