Inspectors have criticised the care of mentally ill inmates at Feltham Young Offenders Institution in west London.
Zahid died days after the assault from massive injuries
A judicial inquiry is being held into the racist murder of Asian inmate Zahid Mubarek by his white cellmate, who had a personality disorder, five years ago.
Anne Owers, chief Inspector of Prisons, said progress had been made in race relations since but that more work was needed on safety and healthcare.
The Prison Service said it was pleased the progress made had been recognised.
Ms Owers said: "Feltham is undoubtedly a different establishment from the one that attracted so much attention and criticism in the past."
Feltham would continue to need "vigilant management" and "well-supported and engaged staff", she said.
But the west London institution would also need more external support and assistance so it could provide a "stable environment" for the young people it holds.
Mental health care facilities must be made available outside the prison system to assist, she said.
Robert Stewart is serving a life sentence for the murder
She also highlighted inadequacies in the general level of healthcare provision, pointing to the case of one young inmate whose injury to his finger was left untreated for six weeks.
In the end the injury became untreatable.
Inspectors also found anti-bullying procedures were weak and that juvenile offenders from ethnic minority groups were more worried about safety than their white counterparts.
They also reported more negative treatment by staff than white inmates.
But Ms Owers praised Feltham's advances in staff-prisoner relations, race relations, training, education and work with juveniles.
Phil Wheatley, director general of the Prison Service, said Feltham manages some of the most disturbed young offenders in the country.
'Work to do'
Many of these suffer from mental illness and are abusers of hard drugs, he said.
"Despite these considerable challenges Feltham is, without doubt, an improving prison that has made great progress in recent years," he said.
He added that he was pleased this had been recognised.
But he acknowledged there was still a lot of hard work to be done, particularly in the field of healthcare services.
The inquiry into the death of 19-year-old Mr Mubarek, who was beaten to death in his cell the night before he was due to be released, is due to report next year.