Galaxy intrinsic alignment (IA) is a source of both systematic contamination of cosmic shear measurement and its cosmological applications and valuable information on the large-scale structure of the universe and galaxy formation. The self-calibration (SC) method was designed to separate IA from cosmic shear, free of IA modeling. It was first successfully applied to the KiDS450 and KV450 data. We improve the SC method in several aspects and apply it to the DECaLS DR3 shear + photo-z catalog and significantly improve the IA detection to similar to 14 sigma. We find a strong dependence of IA on galaxy color, with strong IA signal (similar to 17.6 sigma) for red galaxies, while the IA signal for blue galaxies is consistent with zero. The detected IAs for red galaxies are in reasonable agreement with the nonlinear tidal alignment model, and the inferred IA amplitude increases with redshift. Our measurements rule out the constant IA amplitude assumption at similar to 3.9 sigma for the red sample. We address the systematics in the SC method carefully and perform several sanity checks. We discuss various caveats, such as redshift/shear calibrations and possible improvements in the measurement, theory, and parameter fitting that will be addressed in future works.