In this paper, a direct preconditioner is proposed for coupling matrix reconfiguration of bandpass filters with irregular couplings using the coefficient-parameter continuation method. With the preconditioner, the continuation method can be effectively used for filter synthesis and model extraction of bandpass filters with irregular couplings. In dealing with practical filters that contain a coupling topology with regular cross couplings introduced intentionally or unintentionally, the proposed preconditioner, being used as the start system in the continuation method, can swiftly lead to the solution that matches the physical realization. The preconditioner is physics-based and can be easily obtained by reconfiguring the regular coupling topology with the conventional method. The continuation process with a coefficient-parameter homotopy for coupling matrix reconfiguration is formulated for the first time, which transforms a coupling matrix in canonical form to that in the desired one with irregular couplings. The convergence of the solution and a bootstrapping approach for dealing with multiple irregular couplings are also discussed. The method provides an enabling tool for robot automatic tuning (RAT) of advanced microwave bandpass filters. Three practical examples are presented, including one synthesis example and two model extraction examples for RAT, demonstrating the effectiveness of the reconfiguration method for practical applications.