We obtained VLA radio total power and polarization maps of a merging pair of galaxies NGC4038/39. The whole system is filled with bright extended radio emission with a high thermal fraction of ⋍ 50% at 10.45 GHz and very strong magnetic fields of ⋍ 20μG. A star-forming region at the southern end of the dark cloud complex extending between the galaxies has highly tangled magnetic fields reaching the strength of ⋍ 30μG, even larger than in both individual galaxies. The polarized components associated with the HI ridge at the base of one of the tidal tails and with the northern complex of dark clouds (weakly forming stars) have been identified. A relic magnetic spiral coincident with the northern galaxy has been found, too. Our data on the magnetic fields combined with those in HI, Hα, X-rays and in far infrared are used as a diagnostic tool to distinguish several physically distinct regions.