  The top quark mass will be determined to high accuracy from the shape of the
ttbar total production cross section in the threshold region at a future linear
e+e- collider. Presently the estimated statistical error in the measurement of
the MSbar mass of the top quark is \sim 50 MeV, while the estimated theoretical
error is 150-200 MeV. In order to reduce the theoretical uncertainty to below
50 MeV, we have recently computed an important part of the higher-order
corrections. We deomonstrate the significance of the calculated correction.
