Let \(S\) be a singular integral operator on the unit circle \(T\). The author calculates the essential norm \(\|S_{a,b}\|_e\) in \(L^2(T)\) of the singular integral operator \(S_{a,b}=aP+bQ\), where \(P=\frac 12 (I+S), Q=\frac 12 (I-S)\) are projections in \(L^2(T)\) and \(a,b \in L^\infty(T)\). Theorem. Let \(a,b \in L^\infty (T)\). Then \[ \|S_{a,b}\|^2_e=\inf_{k\in H^\infty+C}\left\|\frac{|a|^2+|b|^2}{2}+ \sqrt{|a\overline{b}-k|^2+\left(\frac{|a|^2-|b|^2}{2}\right)^2}\right\|_\infty . \tag{1} \] The proof is based on the paper of the author and \textit{T. Yamamoto} [Norms of some singular integral operators and their inverse operators, J. Oper. Theory 40, 185-207 (1998)], where the usual norm \(\|S_{a,b}\|\) of the operator \(S_{a,b}\) was calculated. In that case we have \(\inf_{k\in H^\infty}\) in (1) instead \(\inf_{k\in H^\infty+C}\).