A new independent value for the electron's mass in units of the atomic mass unit is presented, m(e) = 0.000 548 579 909 2(4) u. The value is obtained from our recent measurement of the g factor of the electron in (12)C(5+) in combination with the most recent quantum electrodynamical (QED) predictions. In the QED corrections, terms of order alpha(2) were included by a perturbation expansion in Zalpha. Our total precision is three times better than that of the accepted value for the electron's mass.