The head of the Historical Enquiries Team (HET) is to step down by the end of the month after a U-turn by the Chief Constable.
Members of the Policing Board said they were stunned to get an email saying he was going on September 28, just a day after a heated meeting with the Chief Constable Matt Baggott who had insisted Mr Cox would remain until the end of the year.
DUP board member Jonathan Craig said the move will go to restore some confidence in the HET.
"At the end of the day this is not about David Cox, but the new management which will be appointed, how it will implement the recommendations of the inspectorate report, and how quickly it will implement them."
Inspectors said the unit, established in 2005 to investigate more than 3,000 unresolved killings, treated those caused by members of the security forces less rigorously than deaths attributed to paramilitaries.
The report by Her Majesty's Inspectorate of Constabulary (HMIC) further claimed the team was inconsistent; had serious shortcomings and risked losing the confidence of victims' families.
Following the publication, the Policing Board said it had no confidence in the leadership of the HET.
A PSNI chief superintendent and superintendent will be appointed on September 28 to review all policies, procedures and standards and fulfil all recommendations made in the recent report.
HET's director of the military operations, Paul Johnston, will also leave on the same date when his contract ends.
Mr Craig paid tribute to Mr Cox, who is believed to be on leave at the moment.
"He came in and was asked to do an almost impossible job and attempted to put a system together whilst, not perfect, has reached some level of satisfaction in dealing with criminal activity in the past," he added.