On February 14, a member of the public discovered a dead goshawk on land near Abbey Saint Bathens, in the Lammermuir district of Berwickshire, and reported it to RSPB Scotland.
Forensic examination established the bird had been shot and police were contacted on Thursday.
The news comes after the shooting of another goshawk in the Peebles area on March 2.
Ian Thomson, RSPB Scotland’s Head of Investigations said “Goshawks are one of Scotland’s rarest breeding raptors, with only about 150 breeding pairs. Despite the fact that most of their diet consists of crows, woodpigeons and rabbits, species that are perceived as pests by some farmers and gamekeepers, cases of illegal persecution against this species are not uncommon, depriving people of the opportunity to see this charismatic and spectacular bird of prey.
“We join with the police in asking that if anyone has information about this crime, or other raptor persecution incidents, they contact Police Scotland.”
Police Scotland Wildlife Crime Co-Ordinator, Constable Steven Irvine, said: “Inquiry was already underway into the shooting of the goshawk in March and we are now conducting inquiries into the earlier shooting of the bird in February. These birds are a protected species and unlawfully killing them is a very serious offence. Anyone who can assist with these investigations should contact police immediately.