The new spectrometer of polarized neutrons REMUR has been created and put in operation in the Frank Laboratory of Neutron Physics (JINR, Dubna). The spectrometer is dedicated to investigations of multiplayer structures and surfaces by registering the reflection of polarized neutrons and of the inhomogeneous state of solid matter by measuring the small-angle scattering of polarized neutrons. The spectrometer's working range of neutron wavelengths is 1.5-10 Å. The spectrometer is equipped with a linear position-sensitive detector and a focused supermirror polarization analyzer (fan-like polarization analyzer) with a solid angle of neutron detection of 2.2×10^-4 rad. This article describes the design and the principle of operation of the fan analyzer of neutron polarization together with the results of its tests on a polarized neutron beam.