The Scottish Public Services Ombudsman (SPSO) last week launched an inquiry into whether the ethics body for Scotland's councillors had been correct to exonerate Matheson last year.
The SPSO is to investigate whether the Public Standards Commission (PSC) acted "unreasonably" in clearing Matheson. It has warned the PSC that any "irrationality or illogicality" in its decision could amount to maladministration.
The move follows a complaint last November by the Royal Incorporation of Architects in Scotland (RIAS), which ran the design competition for a £15 million revamp of the square. The contest ended in farce in January 2013 after the judges chose a winner, only for Matheson to immediately announce that the council was abandoning the project.
As the winning design was one Matheson had strongly criticised during the judging, the U-turn led to claims the Labour boss had "thrown his toys out the pram" because his own favourite had been rejected.
It was claimed the process cost taxpayers £100,000 and the architects involved £200,000.
RIAS and others complained to the PSC about Matheson, alleging that he had shown bias and tried to coerce staff into rigging the contest - charges Matheson strongly denied.
The PSC cleared Matheson of breaching the councillors' code of conduct, despite admitting that some points of evidence were "irreconcilable" and others were "insufficient" to establish facts.
RIAS asked the commission to reconsider, but it refused. RIAS then made a five-point complaint to the SPSO, which last week agreed to investigate two of them, including one about the PSC's treatment of whistleblowers.
Although the SPSO cannot declare Matheson guilty of misconduct, it could say the PSC was wrong to clear him, leaving a stain on the Labour leader's record.
The move comes as Matheson faces questions about the decision to opt for a £500,000 temporary makeover of George Square.
Sections of the square, laid just five months ago, are already showing signs of collapse. The council has blamed large events, and says contractors will pay for repairs.
RIAS secretary Neil Baxter welcomed the SPSO's decision to investigate.
A Glasgow City Council spokesman said: "We will give any support to the ombudsman and their investigation that they ask of us."