  The masses of excited nonstrange and strange baryons belonging to the
multiplet $[{\bf 70},1^-]$ are calculated in the $1/N_c$ expansion to order
$1/N_c$ with a new method which allows to considerably reduce the number of
linearly independent operators entering the mass formula. This study represents
an extension to SU(6) of our work on nonstrange baryons, the framework of which
was SU(4).
