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The time stepping finite element method based on the backward Euler's method has been widely used to simulate transient electromagnetic fields. Because of the numerical error of nonlinear iterations, the solutions of the derivative quantities may have very big noisy spikes. We present a modified formulation that reduces significantly the numerical error of the derivative quantities in transient finite element analysis of magnetic field computation. We also present an example that simulates the operation of an induction motor and demonstrates that the new method can successfully remove the spikes in the calculated waveforms of back electromotive force and eddy-current loss.