The Theta+ was searched for via the K+p -> pi+X reaction using the 1.2 GeV/c K+ beam at the K6 beam line of the KEK-PS 12 GeV Proton Synchrotron. In the missing mass spectrum of the K+p -> pi+X reaction, no clear peak structure was observed. Therefore a 90 % C.L. upper limit of 3.5 ub/sr was derived for the differential cross section averaged over 2degree to 22degree in the laboratory frame of the K+p -> pi+Theta+ reaction. This upper limit is much smaller than the theoretical calculation for the t-channel process where a K0* is exchanged. From the present result, either the t-channel process is excluded or the coupling constant of g_{K*NTheta} is quite small.
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