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We generalize BPS Lagrangian method and rederive BPS equations for monopoles and dyons from the Lagrangian of SU(2) Maxwell-Higgs model in four dimensional spacetime. We show that in the BPS Lagrangian method the Gaussslaw constraint does not necessary to be imposed beforehand. We find that the BPS Lagrangian has non-boundary terms which in turn gives us some constraint equations. These constraint equations can be reduced by taking the standard BPS equations for Monopoles and Dyons, which turns out to be the Gausss law constraint in the BPS limit.