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Low-frequency electromagnetic problems are analyzed using the electric field integral equation (EFIE) with loop-star basis functions to alleviate the low-frequency breakdown problem. By constructing the loop-star basis functions with the curvilinear RWG (CRWG) basis and the Buffa-Christiansen (BC) basis, respectively, the recently proposed CalderoÂ¿n multiplicative preconditioner (CMP) is improved to become applicable at low frequencies. The Gram matrix arisen from CRWG loop-star basis and BC loop-star basis is studied in detail. A direct solution approach is introduced to solve the Gram matrix equation. The proposed Calderon preconditioner improves the condition of the EFIE operator at low frequencies, which results in a fast convergence of the preconditioned EFIE system. Several numerical examples demonstrate the fast and mesh-independent convergence of the preconditioned system.