Magnetic Resonance Fingerprinting (MRF) acquisitions with balanced Steady State Free Precession (bSSFP) and spiral trajectories are prone to off-resonance artifacts. These artifacts affect the reconstruction of the tissue maps (T1 and T2). We propose to use a UNet CNN feed with fingerprints corrupted by off-resonance to generate corrected fingerprints with only aliasing in the bSSFP-MRF sequence. The feasibility of the proposed approach was evaluated in simulations and in-vivo brain data. Our method improved the NRMSE values for both quantitative maps T1 and T2. Considerably reducing the effects of the off-resonance by UNet-MRF in comparison to classical bSSFP-MRF.