The announcement by the Northern Ireland Policing Board came weeks after the police force accidentally shared the names and work locations of every member of staff in a major data breach.
The surnames, initials, work location and department of each staff member were included in error in response to a freedom of information request.
The breach was hugely sensitive in Northern Ireland, where police officers are still sporadically targeted by dissident groups in bomb and gun attacks, despite a 1998 peace deal that largely ended sectarian violence in the province.
Byrne faced additional pressure after court last week found he had unlawfully disciplined two junior officers who arrested a victim of a 1992 sectarian shooting in Belfast, while policing a wreath-laying event to mark the anniversary of the attack.
Mr Justice Scoffield said he was persuaded the officers were disciplined to avoid Irish Republicans withdrawing their support for the police force.
The largest pro-British party in the region, the Democratic Unionist Party, last week called for Byrne's resignation. Northern Ireland's police federation, a body to represent officers, said it was considering holding a vote of no-confidence.
(Reporting by Amanda Ferguson; Writing Conor Humphries; Editing by William James)
