The $Theta^+$ pentaquark baryon was searched for via the $pi^-pto K^-X$ reaction in a missing-mass resolution of 1.4 MeV/$c^2$(FWHM) at J-PARC. $pi^-$ meson beams were incident on the liquid hydrogen target with the beam momentum of 1.92 GeV/$c$. No
peak structure corresponding to the $Theta^+$ mass was observed. The upper limit of the production cross section averaged over the scattering angle of 2$^{circ}$ to 15$^{circ}$ in the laboratory frame was obtained to be 0.26 $mu$b/sr in the mass region of 1.51$-$1.55 GeV/$c^2$.The upper limit of the $Theta^+$ decay width using the effective Lagrangian approach was obtained to be 0.72 MeV/$c^2$ and 3.1 MeV/$c^2$ for $J^P_{Theta}=1/2^+$ and $J^P_{Theta}=1/2^-$, respectively.
