Carrie Marr, the wife of NHS Tayside CEO Gerry Marr, was put in charge of a key directorate without the job being externally or internally advertised.
A spokeswoman for the board said the appointment was made in line with the body's policies.
NHS Tayside has already been at the centre of damaging allegations that staff manipulated waiting-time targets by marking patients as "unavailable" for treatment.
An audit last month confirmed the practice, with a spokesman for the board noting: "We very much regret that this has happened, apologise to patients and reassure them that we have put controls in place to ensure these practices have been eradicated."
The board, which delivers healthcare to around 400,000 people, also attracted criticism over plans to cut the level of emergency surgery provision at Perth Royal Infirmary.
The Sunday Herald can reveal that NHS Tayside's internal appointments process for senior staff is now also under the microscope.
In early 2011, Gerry Marr secured a promotion to become the body's chief executive. At the time, his wife, Carrie, was "associate director" of the change and innovation team.
After Mr Marr's appointment, the board started a restructuring that resulted in his wife and her colleagues being transferred over to a new body, the Tayside Centre for Organisational Effectiveness (TCOE).
The board decided to make TCOE a stand-alone directorate in its own right and agreed to appoint a director in August 2011, a job that was given to the chief executive's wife.
Mrs Marr was "matched" to the new role and her previous responsibilities were "subsumed" within the new director's post, a decision made by the board's remuneration committee.
Mr Marr – whose salary for 2011 was between £170,000 and £175,000 – left the committee meeting before the matter was discussed. This process required no external or internal advertising process.
The new role has given Mrs Marr more power and responsibility. No details are available of her current salary, although the promotion did not include a pay rise.
She is now the head of a directorate, where before she only had a senior role in another part of the organisation.
The TCOE, set up to "improve patient services and develop an organisational ability to undertake ongoing cycles of change and innovation", reports to a committee Mr Marr sits on.
SNP MSP John Wilson said: "The revelation that the wife of the chief executive of NHS Tayside was appointed to a post with greater responsibilities, which was not subject to any semblance of open recruitment, goes completely against the expectation that there should be transparency in the public appointments process.
"This latest disclosure also follows on from the disclosure that NHS Tayside manipulated its hospital waiting-time figures.
"The Scottish Government should call on all public bodies to tighten their recruitment procedures to ensure that all such appointments are open and transparent."
A spokesperson for NHS Tayside said: "A full meeting of the Tayside NHS board approved TCOE as a stand-alone directorate within NHS Tayside in June 2011 and the board agreed to appoint a director of TCOE in August 2011.
"Under NHS Tayside organisational change policy, which applies to all members of staff, it was identified that the responsibilities of the associate director for change and innovation would be subsumed within the new TCOE director's work portfolio and, therefore, in line with the policy, the existing postholder would be matched to the new post."