Justice secretary Humza Yousaf has told MSPs he plans to ask Her Majesty's Chief Inspector of Prisons to "undertake external assurance" of the Scottish Prison Service's (SPS) review, following a fatal accident inquiry (FAI) into the death.
Allan Marshall was remanded in custody in HMP Edinburgh in Saughton, having being charged with using threatening or abusive behaviour and threatening or impeding police, when he died of a cardiac arrest while being restrained by several officers on 28 March 2015.
He made 13 recommendations, including ensuring prison officers received proper training while also having the presence of a first responder in any future cases.
Now, Mr Yousaf has written to Holyrood's Justice Committee to update them on actions taken in response to the FAI.
He expressed his sympathies and condolences to Mr Marshall's family, adding "it is concerning to note the Sheriff's determination concludes that, in this tragic incident, there were defects in the system that contributed to the outcome".
Mr Yousaf said the Crown counsel determined there would be no criminal proceedings after a criminal investigation into Mr Marshall's death.
He said SPS brought in additional staff training immediately following Mr Marshall's death and has set up a working group to address the FAI recommendations, "paying particular attention to the recognition and understanding of medical conditions which may be triggered or exacerbated by the use of restraint".
The letter continues: "SPS has also acknowledged the need for external assurance of this review process.
"Therefore, I have advised Her Majesty's Chief Inspector of Prisons today that I will write to her formally this week asking her to undertake external assurance of the SPS's review of C&R training and actions following from the FAI recommendations, in conjunction with relevant independent experts, as required."
He concluded: "Any death in our care is a tragedy and I am determined that our justice system continues to learn and improve so we can avoid such tragedies from happening again in the future."