The Labour councillor was attacked by his SNP opponents for failing to comply with advice from Audit Scotland that elected members should screen severance deals for high-paid officials.
Mr Matheson's administration has paid off many senior directors over the past two years under a multi-million-pound round of early retirements approved in 2009 and ending now.
However, Mr Matheson and other councillors have left decisions on large exit packages – some costing hundreds of thousands of pounds – to senior officials.
The Herald can reveal Audit Scotland flagged up a "risk" that councillors were not involved in making decisions over early retirements for individual senior staff back in September 2010.
The watchdog advised councillors across Scotland to keep tight controls over such deals for years and spelled out its guidelines in a 2003 policy called "Bye Now, Pay Later".
In September 2010 Audit Scotland told the council: "There is a risk that members are not able to discuss and agree potentially contentious retirement/redundancy decisions prior to their approval."
The local authority responded by saying that councillors had approved the local authority's overall redundancy policy and that "in future members will be made aware of redundancy and recruitment costs associated with senior officers".
Mr Matheson did not comment. However, a spokesman said councillors would screen any exit package for senior officials under a new round of voluntary redundancies and early retirements for the new year. The spokesman said: "Bye Now, Pay Later recommended that members be involved in redundancy and early retirement decisions for senior officers.
"Members did approve our scheme in November 2009. When Audit Scotland considered our scheme in 2010, it recommended members should be further involved. However, our scheme had already been agreed by members. Future schemes will address that."
Graeme Hendry, the leader of the SNP on Glasgow City Council, said: "It would seem clear that Audit Scotland recommended that councillors should be involved in approving voluntary severance for early packages.
"Instead of implementing this, Councillor Matheson has stuck his head in the sand, resulting in millions being spent on voluntary severance packages without any business case to show savings."
Mr Hendry has written to Audit Scotland calling for exit packages for senior officers to be investigated.
He stresses he does not believe any individual official has done anything wrong by taking a deal.