  Koplienko gave a trace formula for perturbations of self-adjoint operators by
operators of Hilbert-Schmidt class $\mathcal{B}_2(\mathcal{H})$. Recently
Gesztesy, Pushnitski and Simon gave an alternative proof of the trace formula
when the operators involved are bounded. In this article, we give a still
another proof and extend the formula for unbounded case by reducing the problem
to a finite dimensional one as in the proof of Krein trace formula by
Voiculescu, Sinha and Mohapatra.
