Appeal judges in Edinburgh have rejected an attempt to take an appeal against the Lockerbie bomber to the UK's highest court.
Abdelbaset al-Megrahi was convicted over the bombing of Pan Am flight 103 in December 1988.
In January, Court of Appeal judges rejected a third appeal against his conviction, which was made by his son.
In this latest action his family sought permission to take the appeal to the UK Supreme Court.
Megrahi is the only person to have been convicted over the bombing.
All 259 passengers and crew on board the flight were killed, along with 11 people in Lockerbie who died when the wreckage fell onto their homes.
Former Libyan intelligence officer Megrahi was found guilty in 2001 of mass murder and jailed for life with a minimum term of 27 years.
The latest legal bid, asking permission to appeal to the UK Supreme Court, was refused by five Scottish judges.
Aamer Anwar, the family's lawyer, said they would now seek leave to appeal directly to the UK Supreme Court, the final court of appeal for the case.
A written judgment issued on Thursday by Lord Carloway, the Lord Justice General, said the court "has had some difficulty in understanding the exact nature of the challenge".
It said: "Although the case is clearly one of public importance, the proposed grounds of appeal do not raise points of law of general public importance.
"The principles of law which the court applied were all well known, settled and largely uncontroversial in the appeal.
"For these reasons, the court refuses permission to appeal to the UK Supreme Court."
In December, the US announced new charges against a Libyan man who is accused of making the bomb.
Abu Agila Mohammad Masud has been charged with terrorism-related crimes, and prosecutors say they will seek his extradition to stand trial in the US.
Megrahi was released from prison in 2009 on compassionate grounds while terminally ill with cancer, and died in Libya in 2012.
The third appeal was lodged after the Scottish Criminal Cases Review Commission (SCCRC) referred the case to the High Court in March 2020, ruling that a possible miscarriage of justice may have occurred.
Judges then granted his son, Ali al-Megrahi, permission to proceed with the appeal in relation to the argument "no reasonable jury" could have returned the verdict the court did, and on the grounds of non-disclosure of documents by the Crown.
Appeal court judges in January rejected both grounds of appeal, which means his conviction stands.
Ali Al-Megrahi said: "I have now instructed our legal team to seek leave to appeal directly to the UK Supreme Court which is the final court of appeal for my father's case.
"It is time for a new Libya, but that will never happen until there is justice for those who died in Lockerbie. I regard my father Abdelbaset Al-Megrahi as the 271st victim of Lockerbie.
"We now have a new democratic government and we look to them to support our legal team in their pursuit of justice."
Mr Anwar said: "I have no doubt that the new democratic Libyan Government headed by Abdul Hamid Aldabaibai will support this final appeal for justice on behalf of the Al-Megrahi family and help in our efforts to prove the innocence of Libya and its people."
Lockerbie's legal timeline
US and British investigators indicted Megrahi in 1991 but he was not handed over by the Libyans until April 1999.
May 2000 - A special trial under Scots law starts on neutral ground at Camp Zeist in the Netherlands.
31 January 2001 - Former Libyan intelligence officer Megrahi is found guilty of mass murder and jailed for life with a minimum term of 27 years.
March 2002 - Megrahi loses an appeal against his conviction.
June 2007 - The Scottish Criminal Cases Review Commission (SCCRC) recommends that Megrahi is granted a second appeal against his conviction.
18 August 2009 - Megrahi's move to drop his second appeal is accepted by judges at the High Court in Edinburgh.
20 August 2009 - Megrahi, who has terminal prostate cancer, is released from prison on compassionate grounds.
May 2012 - Megrahi dies at his home in Tripoli, aged 60.
July 2017 - Megrahi's family launch a new bid to appeal against his conviction.
March 2020 - The Scottish Criminal Case Review Commission says Megrahi's conviction can be taken to a fresh appeal.
August 2020 - The posthumous appeal is given permission to proceed.
January 2021 - Judges uphold the verdict of the trial and reject the appeal.
April 2021 - Appeal judges in Edinburgh reject an attempt to take the appeal to the UK Supreme Court.