A new simple formulation of absorbing boundary conditions with higher order approximation is proposed for the solution of Maxwell's equations with the finite-difference time-domain (FD-TD) method. Although this higher order approximation is based on the third order approximation of the one-way wave equations, we have succeeded in reducing it to an equation in a form quite similar to the second order appoximation. Numerical tests exhibit smaller reflection errors than the prevalent second order approximation.