  We present an improved measurement of CP-violating asymmetries in B0 -> pi+
pi- decays based on a 78 fb^-1 data sample collected at the Y(4S) resonance
with the Belle detector at the KEKB asymmetric-energy e+e- collider. We
reconstruct one neutral B meson as a B0 -> pi+ pi- CP eigenstate and identify
the flavor of the accompanying B meson from inclusive properties of its decay
products. We apply an unbinned maximum likelihood fit to the distribution of
the time intervals between the two B meson decay points. The fit yields the
CP-violating asymmetry amplitudes Apipi = +0.77+/-0.27(stat)+/-0.08(syst) and
Spipi = -1.23+/-0.41(stat)+0.08/-0.07(syst), where the statistical
uncertainties are determined from Monte Carlo pseudo-experiments. We obtain
confidence intervals for CP-violating asymmetry parameters Apipi and Spipi
based on a frequentist approach. We rule out the CP-conserving case,
Apipi=Spipi=0, at the 99.93% confidence level. We discuss how these results
constrain the value of the CKM angle phi2.
