  We report on a search for D0-D0B mixing made by studying the `wrong-sign'
process D0->K^+pi^-. The data come from an integrated luminosity of 9.0 1/fb of
e^+e^- collisions at s^(1/2) of approximately 10 GeV recorded with the CLEO
II.V detector. We measure the time integrated rate of the `wrong-sign' process
D0->K^+pi^- relative to that of the Cabibbo-favored process D0B->K^+pi^- to be
R=(0.332^{+0.063}_{-0.065}+-0.040)%. We study D0->K^+pi^- as a function of
decay time to distinguish direct doubly Cabibbo-suppressed decay from D0-D0B
mixing. The amplitudes that describe D0-D0B mixing, x' and y', are consistent
with zero. At the 95% C.L. and without assumptions concerning charge-parity
(CP) violating parameters, we find (1/2)x'^2 < 0.041% and -5.8% < y' < 1.0%.
