We performed an improved search for $ u_mu to u_e$ oscillation with the KEK to Kamioka (K2K) long-baseline neutrino oscillation experiment, using the full data sample of $9.2 times 10^{19}$xspace protons on target. No evidence for a $ u_e$ appearance signal was found, and we set bounds on the $ u_mu to u_e$ oscillation parameters. At $Delta m^2$ = $2.8 times 10^{-3} mathrm{eV}^2$, the best fit value of the K2K $ u_mu$ disappearance analysis, we set an upper limit of $sin^2 2theta_{mu e}$ $<$ 0.13 at 90% confidence level.
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