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The Muon Ionization Cooling Experiment (MICE) will demonstrate ionization cooling in a short section of a realistic cooling channel using a muon beam at Rutherford Appleton Laboratory in the UK. The coupling magnet is a superconducting solenoid mounted around four 201 MHz RF cavities, which produces magnetic field up to 2.6 T on the magnet centerline to keep muons within the iris of RF cavities windows. The coupling coil with inner radius of 750 mm, length of 285 mm and thickness of 102.5 mm will be cooled by a pair of 1.5 W at 4.2 K small coolers. This paper will introduce the updated engineering design of the coupling magnet made by ICST in China. The detailed analyses on magnetic fields, stresses induced during the processes of winding, cool down and charging, and cold mass support assembly are presented as well. [ABSTRACT FROM AUTHOR]