An NHS trust which said a girl's fatal stabbing by a psychiatric patient could not have been prevented has been criticised in an independent review.
Seven-year-old Emily Jones was attacked in front of her parents by Eltiona Skana in a Bolton park in March 2020.
Skana, 32, admitted manslaughter on the grounds of diminished responsibility and is detained indefinitely.
NHS England said Greater Manchester Mental Health NHS Foundation Trust had been wrong to reach that conclusion.
The trust accepted the review's findings and promised to learn lessons.
Skana's trial heard she had been sitting alone on a bench in Queen's Park when Emily rode past her on a scooter on Mother's Day.
Skana then grabbed Emily before slitting her throat with a craft knife.
After Emily's death, Greater Manchester Mental Health NHS Foundation Trust's (GMMH) internal review concluded it was "difficult to see how this incident could have been prevented".
But NHS England has responded: "We do not believe that the report provides sufficient analysis to justify this conclusion."
Its own investigation found Skana, who has paranoid schizophrenia, was "potentially dangerous when unwell" and that "it was clear by 2017 that [she] presented risks to others when she was ill, but not when she was well."
And while Skana "showed varying degrees of compliance... it was also clear that she became unwell when she was not taking medication as prescribed."
The report said: "Our most important finding is that the trust's understanding of risk concepts was poor."
Skana had first been referred by her GP to GMMH in 2014.
She was diagnosed with acute schizophrenia-like psychotic symptoms a year later, after being found holding a knife.
In 2017 and while continuing to receive treatment, Skana was temporarily admitted to hospital after attacking a relative with an iron.
Earlier this year, Emily's father Mark Jones described the GMMH report as "insulting", adding that he had "no confidence in the way mental health is dealt with".
The NHS England review said "it was evident that the trust had not fully 'bottomed out' clinical aspects of the case - in particular in relation to [Skana's] medication."
It also said "the trust should review its risk policy" and prominently display a "concise summary of the risks of each patient" on their record.
GMMH chief executive Neil Thwaite said: "We accept the findings of the external review into the tragic incident."
He said the report's recommendations "will be actioned as a highest priority and regularly reviewed".