Speaking at the Edinburgh international book festival, Baksi repeated claims that he has witnessed the manuscript and that the fourth book in the popular crime fiction series gives a prominent role to hacker-heroine Lisbeth Salander's twin sister Camilla.
"It is at 260 pages at the moment – about 70 percent complete. Eva has said the book is not so complete. She took the book after Stieg died and showed it to me and his father," he said, according to a report in the Guardian daily.
It has been widely reported that when Stieg Larsson died suddenly on November 9th, 2004 that he had plans for a series of five or six books within the Millennium series.
Eva Gabrielsson, Larsson's partner for 30 years, has indicated that a large part of a fourth manuscript is contained in a computer left to her as part of Larsson's personal effects.
In her biography of their life together "Stieg and I" (Stieg och jag), Gabrielsson has given the book the working title "God's revenge" (Guds hämnd).
The contents of the computer have featured from time to time in the bitter struggle between Gabrielsson and Stieg Larsson's father and brother who instead inherited what became the large part of his estate due to the fact that the couple had not formally married nor completed a will.
Gabrielsson has however meanwhile claimed that the book is at most 30 percent complete and has also taken offence at Baksi's portrayal of her dead partner's journalistic skills in his own memoir "Stieg Larsson My Friend", which he was in Edinburgh to promote.
In an interview with the Expressen daily in March, Baksi revealed that the book holds a number of plot twists and turns, speaking at the annual book fair in the Scottish capital he gave further details.
Lisbeth Salander's estranged sister Camilla featured only fleetingly in "The Girl Who Played With Fire" - the second of the published trilogy - but, according to Baksi, the twin's character is given more prominence in the fourth novel.
The success of the Millennium books has been unprecedented for a Swedish writer and Baksi told the Edinburgh book meet that the fourth book would be ideally suited to becoming a Hollywood film with a plot taking the characters to Sweden, Canada, Greenland and Ireland.