[en] Construction of the Rare-RI Ring to measure masses of short-lived rare-RI with a relative precision of 10⁻⁶ is in progress at RIKEN. The Rare-RI Ring consists of six sectors where each sector consists of four dipole magnets. Since the mass measurement is done by the isochronous mass spectrometry in the Rare-RI Ring, creating isochronous magnetic field is one of the important issues in mass measurements with the Rare-RI Ring. In order to make an isochronous field, we installed ten trim coils in the two outer dipoles among the four dipoles in each sector magnet. The isochronism of the magnetic field have been confirmed by measuring time-of-flight (TOF) of alpha particles from an alpha-source (²⁴¹Am). We measured TOF of alpha particles while changing the radial gradient of the magnetic field by trim coils and evaluated the isochronism from standard deviation of the TOF spectrum. The TOF width is minimum for a radial gradient of magnetic field ($\mathrm{\partial <!--\; ???\; -->}{B}_z$/$\mathrm{\partial <!--\; ???\; -->}r$)/B₀ = 0.205 m⁻¹, which is in good agreement with the simulated value. (paper)