In a closed session, a majority of present board members voted in favor of approving interim superintendent Reuben Mills' recommendation to hire Valore as Camden's coach by a 4-1 margin, with two abstentions.
But because Valore's hiring was an "appointment," a majority vote of the full board of nine members was needed.
Two board members were not present at Tuesday night's meeting.
Blackshear cast the "no" vote.
Asked why she voted against the recommendation, Blackshear said, "It was no color thing," an apparent reference to the fact that Valore would have been Camden's first non-African American coach since Tony Alfano retired after the 1970 season.
"I just didn't like the way it was done," Blackshear said.
Mills declined to comment after the meeting.
Blackshear said "the administration" needs to come up with another candidate to become Camden's fifth coach since legendary coach Clarence Turner retired for health reasons during the 2008 season.
Byrd, who led Camden to South Jersey Group 3 titles in his first two seasons, plans to "fight" to return as Panthers coach, according to a source close to the former coach.
Byrd has been suspended for the 2013-14 season by Camden administrators for allowing an independent filmmaker access to the team during the 2011-12 season without board of education approval.
Turner said, "We need to have a coach," stressing the importance in creating some stability around the program before summer workouts.
A couple of speakers during the public portion of the meeting were highly critical of Mills' recommendation to hire Valore.
Valore and Byrd were unavailable for comment Tuesday night.
Valore was the coach at Cherry Hill East from 1977 to 2011 and was head coach at Cumberland Regional last season.
Valore is believed to have the support of Camden athletic director Mark Phillips as well as Mills and some former star Camden players such as 2000 graduate Arthur Barclay.
Byrd, a Camden graduate who teaches in the Pennsauken school district, was 39-24 in two seasons. He took over a struggling team that had compiled an 8-18 record in 2010-11.
Valore, who won 549 games in 35 seasons at Cherry Hill East, emerged as the leading candidate after interviewing with Mills and Phillips on May 17.
However, sources indicated that the city was abuzz over the holiday weekend after word surfaced that Valore would be named the new coach, with some high-ranking political figures expressing concern.
The Valore situation apparently was complicated by concern on the part of some Camden basketball supporters and others in the community over the circumstances of the suspension of Byrd, a 1988 Camden graduate.
Byrd's supporters believe that a season's suspension was too severe of a punishment, especially since two of his supervisors, Phillips and principal James Thompson, appeared in the film.
Current Cherry Hill East coach Dave Allen, a former player and assistant coach under Valore, called Valore "one of the finest men I know."
Allen said Valore would be a great coach for the Camden program.
"He's one of the best teachers and coaches I've ever seen," Allen said.
Contact Phil Anastasia at firstname.lastname@example.org. Follow on Twitter @PhilAnastasia. Read his blog, "Jersey Side Sports," at www.inquirer.com/