The general-purpose Compact Muon Solenoid (CMS) detector at the Large Hadron Collider (LHC) at CERN studies a production of new particles in the proton-proton collisions at the LHC center of mass energy 13.6 TeV. The detector includes the magnet based on the 6 m diameter superconducting solenoid coil operating with the current of 18.164 kA. This current creates a central magnetic flux density of 3.8 T that allows to measure momenta of the produced in collisions charged particles with tracking and muon subdetectors at a high precision. The CMS magnet contains a 10,000 ton flux-return yoke made of construction steel that bends muons in steel blocks magnetized with the solenoid returned magnetic flux. To reconstruct the muon trajectories, and thus, to measure the muon momenta, the drift tube and cathode strip chambers are located between the layers of the steel blocks and serve for this purpose. To describe the distribution of the magnetic flux in the magnet yoke layers, a three-dimensional computer model of the CMS magnet is used. To prove the calculations, the special measurements are performed with the flux loops wound in 22 cross-sections of the flux-return yoke blocks. The measured voltages induced in the flux loops during the CMS magnet ramp ups and downs, as well as during the superconducting coil fast discharges with the 190 s time constant, are integrated over time to obtain the initial magnetic flux densities in the flux loop cross-sections. The measurements obtained during the seven standard ramp downs of the magnet have been analyzed in 2018. From that time three fast discharges are occurred during the standard ramp downs of the magnet. This allows to single out the contributions of the eddy currents, induced in steel, to the flux loop voltages registered during the fast discharges of the coil. Accounting for these contributions to the flux loop measurements during manually triggered fast discharges in 2006 allows to perform the validation of the CMS magnet computer model with a better precision. The technique of the flux loop measurements, and the obtained results are presented and discussed.