Electromagnetic problems can be solved by using the integral form of Maxwell equations. The Surface Partial Element Equivalent Circuit (S-PEEC) method is an integral equation-based method that is suitable when high-frequency effects, such as skin and proximity effect, are dominant. However, the computation of interaction quadruple integrals is computationally expensive and numerically unstable due to singularities. In previous work, we proved how to decouple one of the quadruple integrals, and showed the gaining in stability and computational time. In this work, we extend the result to the second integral with the curl of the Green's function. Numerical examples prove the acceleration in terms of computational time achieved with the proposed approach. Future work will focus on integration strategy and further optimization of the proposed algorithm.