Companies must be independent to be certified for the city's Disadvantaged Business Enterprise program.
The school, which does not have a senior class yet, earns a B grade in state scoring.
Carla Major follows several other longtime members who left.
Friday afternoon's session focused on Safety and Permits and one of its divisions, the Taxicab Bureau.
In March, months before it sued oil and gas companies, the levee authority knew the state would pull its funding.
Schools for students with special circumstances do not perform well in state evaluations under current criteria.
The building has been appraised for $4.5 million, but local and state governments have loaned the project more than $9 million.
A move into the former St. Rose de Lima site on Bayou Road is being discussed.
Of the seven A schools in the city, just one buses its students. That means some students fortunate enough to get into one of the best schools must take hours-long rides on public transportation, making them and their parents uneasy.
Board will hold a special meeting next week to consider extension for Keith Bartlett.