Fully relativistic calculations have been performed for two multiplets, $3s3p^2\;^4P$ and $3s3p4s\;^4P^o$, in Al I. Wave functions were obtained for all levels of these multiplets using the GRASP programs. Reported are the E1 transitions rates for all transitions between levels of these multiplets. Transition energies and transition rates are compared with observed values and other theory. Our calculated transition rates are smaller by about 10% than observed rates, reducing a large discrepancy between earlier calculations and experiment.