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The man found guilty of the Kent hammer murders of Lin and Megan Russell, and the attempted murder of Josie Russell, has been refused a new appeal.
Michael Stone, formerly of Skinner Street, Gillingham, was originally convicted of the 1996 attacks in 1998 and then again at a retrial three years later.
Mrs Russell and her two daughters were targeted by Stone in Chillenden.
Stone is serving three life sentences for the hammer attacks.
A spokesman for the Criminal Cases Review Commission said: "After a detailed and painstaking investigation we have identified nothing which justifies referring the case for a new appeal.
"The Commission’s role is to independently review alleged miscarriages of justice.
"Where we identify new evidence or new legal argument which we consider raises a real possibility that the appeal court would quash a conviction as unsafe, we have the power to refer the case for a fresh appeal.
"In Mr Stone’s case we have not found any new evidence or new argument that we consider capable of raising a real possibility that the conviction would be quashed."