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

New look at the $[{\bf 70},1^-]$ nonstrange and strange baryons in the $1/N_c$ expansion