Police said the three-page handwritten note found in the hotel room from which the 51-year-old executive plunged to his death, was written by his wife Sally.
Police said Slym could have taken the extreme step after reading the note by his wife of 30 years that mentioned domestic problems.
The note was written by Sally Slym. The couple had had an argument. It is her writing, Police Lieutenant Somyot Booyakaew said, noting that it was not a suicide note by the victim. He did not give further details.
Somyot reiterated that Slyms death was not a murder. Police now believe Slym must have jumped through an open window in his 22nd floor suite at the Shangri-la Hotel as the opening was too small for a person to slip through and fall.
The suite has a huge sealed window overlooking the Chao Praya River and a small nearby window that can be opened.
Slym died from the impact of the fall, which fractured his skull. The British nationals body was found on Sunday by the staff of the hotel on the balcony of the fourth floor.