Long-term current drift and dielectric relaxation in organic thin films of a single-layer structure pose a serious problem for the accurate measurement of magnetoresistance at low magnetic fields. A new measurement scheme was devised to minimize errors and to report that the magnetoresistance in tris(8-hydroxyquinolinato)aluminum obeys a power law on the magnetic field at 300, 100, and 4.2 K in an entire range from 1 to 140 mT. The exponent of the power increases gradually from 0.47 for a bias voltage of 3 V to 0.58 for a bias voltage of 8 V. The magnetoresistance was observable above the threshold voltage only and its sign was always negative. (C) 2012 Elsevier B.V. All rights reserved.