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A higher-order Nyström scheme is developed for the marching-on-in-degree (MOD) solution of the time-domain magnetic field integral equation (TDMFIE) for the analysis of transient electromagentic scattering from a three-dimensional closed conducting object of arbitrary shape. In this method, the surface of the object is discretized into curvilinear triangular patches and the Lagrange interpolation polynomials are utilized to expand the spatial variation of the unknown electric current density in the TDMFIE. The transient variation of the electric current density is expanded in terms of the weighted Laguerre polynomials. With the use of the point-matching spatial and Galerkin temporal testing procedures, the proposed algorithm overcomes the late-time instability problem that often occurs in the marching-on-in-time (MOT) approach. Numerical results are presented to show that the proposed algorithm exhibits a good accuracy, a highly efficient computation of the impedance matrices, and a higher-order convergence with regard to the spatial discretization.