  We report an improved measurement of the partial-rate CP asymmetry in B+ =>
K0pi+ and B- => K0bar pi- decays. The analysis is based on a data sample of 85
million BBbar pairs collected at the Upsilon(4S) resonance with the Belle
detector at the KEKB e+ e- storage ring. We measure Acp(K0pi+-) = 0.07^{+0.09
+0.01}_{-0.08 -0.03}, where the first and second errors are statistical and
systematic, respectively; the corresponding 90% confidence-level interval is
-0.10 < Acp(K0pi+-) < 0.22 .
