Councillor Baird was suspended by the SNP Group for failing to follow procedure by not presenting them with a motion he wished to make to a full meeting of North Lanarkshire Council.
The motion called for additional CCTV to be installed in buildings and on transport to protect addition support needs pupils.
Councillor Baird previously told the Times & Speaker he still regards himself as an SNP councillor, the matter will be dealt with later in the summer with the council currently on recess.
Councillor Beveridge, who quit the SNP in 2015, was happy to second the motion.
He said: “I had the honour of seconding a motion by Councillor David Baird, a councillor with conviction for doing the right thing and supporting families and workers in our ASN schools.
“The motion looked at installing CCTV cameras in certain areas of ASN schools, to safeguard pupils and staff.
“Democracy in action, all political group councillors voted against this motion preferring an amended motion, which is there democratic right so to do.
“Independent councillors, free from party whips, voted in favour of the motion.
“However as a result of not obeying the SNP masters Councillor Baird has been suspended from the Group.
“It takes courage to do the right thing and I applaud Councillor Baird as he could easily have done the sheepish thing and withdrew this motion.
“However he has shown that his values as an elected representative of the people means more to him than being part of a political cabal.”