We report the discovery of a coherent magnetic spiral structure within the nearby ringed Sab galaxy NGC 4736. High-sensitivity radio polarimetric data obtained with the VLA at 8.46 and 4.86 GHz show a distinct ring of total radio emission precisely corresponding to the bright inner pseudoring visible in other wavelengths. However, unlike the total radio emission, the polarized radio emission reveals a clear pattern of ordered magnetic field of spiral shape, emerging from the galactic center. The magnetic vectors do not follow the tightly wrapped spiral arms that characterize the inner pseudoring, but instead cross the ring with a constant and large pitch angle of about 35 degrees. The ordered field is thus not locally adjusted to the pattern of star formation activity, unlike what is usually observed in grand-design spirals. The observed asymmetric distribution of Faraday rotation suggests the possible action of a large-scale MHD dynamo. The strong magnetic total and regular field within the ring ( up to 30 and 13 mu G, respectively) indicates that a highly efficient process of magnetic field amplification is under way, probably related to secular evolutionary processes in the galaxy.