The missing mass spectroscopy of Ξ − hypernuclei is planned at the Japan Proton Accelerator Research Complex (J-PARC) by using the (K − , K + ) reaction. We are constructing a new magnetic spectrometer, S-2S, which has a better momentum resolution [∆p/p = 5 × 10 −4 (FHWM)] than that of an existing spectrometer (SKS) at J-PARC. S-2S would give us an opportunity to confirm the existence of Ξ − hypernucleus as a peak structure owing to both the high momentum resolution and its reasonably large solid angle. Brief descriptions of our experiment and of its preparation status are presented in this article.