We report the results of a photoluminescence (PL) study of the properties of a bound-exciton (BE) line observed at about 3838Angstrom in the PL spectrum of 4H-SiC and at 4182Angstrom in 6H-SiC. Both spectra have almost the same phonon structure containing localized modes. The temperature dependences show that the no-phonon (NP) lines have at least three excited states higher in energy. The most intense high-temperature lines do not split under applied magnetic field whereas the low temperature lines split into three components when the magnetic field is applied in the direction perpendicular to the c-axis. Time-resolved PL reveals several hundreds microseconds long lifetime at 2K with a second component an order of magnitude faster. Our results can be explained by an excitonic recombination at an isoelectronic center but are in conflict with the previous association of the 3838Angstrom line in 4H-SiC with the recombination of the bound exciton at the neutral shallow boron acceptor. The luminescence in our samples is increasing with excitation time. This luminescence is not observed from our as-grown material but appears after SIMS analysis. The as-grown material used was intentionally boron-doped epilayers.