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Muon beams are generated with large transverse and longitudinal emittances. In order to achieve the low emittances required by a muon collider, within the short lifetime of the muons, ionization cooling is required. Cooling schemes have been developed to reduce the muon beam 6D emittances to ≈300  μm-rad in transverse and ≈1–1.5  mm in longitudinal dimensions. The transverse emittance has to be further reduced to ≈50–25  μm-rad with an upper limit on the longitudinal emittance of ≈76  mm in order to meet the high-energy muon collider luminosity requirements. Earlier studies of the transverse cooling of low energy muon beams in high field magnets showed a promising performance, but did not include transverse or longitudinal matching between the stages. In this study we present the first complete design of the high field-low energy ionization cooling channel with transverse and longitudinal matching. The channel design was based on strong focusing solenoids with fields of 25–30 T and low momentum muon beam starting at 135  MeV/c and gradually decreasing. The cooling channel design presented here is the first to reach ≈50 micron scale emittance beam. We present the channel’s optimized design parameters including the focusing solenoid fields, absorber parameters and the transverse and longitudinal matching.