A 220 m long ionization cooling system consisting of three solenoids with two field-flip sections, is proposed as a cooling channel for the neutrino factory. The reduction of transverse emittance is achieved using 87 liquid hydrogen absorbers (30-40 cm long), and 87 (2 m long) 200 MHz linacs. The first flip is performed at relatively small magnetic field, B = 3 T, to keep the longitudinal motion under control. The field is then increased adiabatically up to 7 T and a second field flip performed. The cooler was studied and simulated in detail. Preceded by a 16 GeV proton driver, a carbon target, a mini-cooler and a buncher, the system provides about 0.082 muons per incident proton.