In this work we investigate the finite element preconditioning method for the C¹-cubic spline collocation discretizations for an elliptic operator A defined by Au := -Δu + a₁u_x + a₂u_y + a₀u in the unit square with some boundary conditions. We compute the condition number and the numerical solution of the preconditioning system for the several example problems. Finally, we compare the this preconditioning system with the another preconditioning system. AMS Mathematics Subject Classification : 65N30, 65N35, 65F05, 65F10