An independent investigation has found a catalogue of failures in Humber Mental Health Teaching Trust's care of Benjamin Holiday, 25, a paranoid schizophrenic who stabbed a mother-of -five to death .
The trust has also apologised after being criticised over the care of a mentally-ill man, Michael Torrie, 43, who killed his elderly mother in 2003.
BRANWEN JEFFREYS, BBC HEALTH CORRESPONDENT
The number of homicides by people with mental health problems has remained fairly constant at around 50 a year since the 1950s. In the same time frame homicides overall have roughly tripled.
Mental health charities have frequently expressed their frustration that this fact is overlooked in the coverage of individual murders, however shocking and avoidable these cases might be.
The level of public anxiety about the risk of violence from people with mental health problems is measured by the Department of Health in England as part of a wider survey of attitudes. It suggests a third of people think someone with a mental health problem is likely to be violent.
The public perception of the risk of random violence from someone with mental health issues appears to be out of step with reality.
The National Confidential Inquiry which looks at homicides by people with mental illness has found that random attacks on a stranger account for just 1% of homicides in England and Wales each year, around five in total.
This is supported by academic research in this area.
One study which looked at all people charged with homicide in England and Wales over almost 30 years found that people with mental illnesses are three times more likely to kill someone they know than a stranger.
None of this is any consolation to the friends or relatives of those killed by someone with mental illness.
In some individual cases, but not all, failings have been found in the mental health services. The provision of most mental health care in the community has made risk assessment increasingly important, and some inquiries have highlighted failings in communication.
For the wider public these figures should be a reassuring reminder that these events are rare.
MARJORIE WALLACE, MENTAL HEALTH CHARITY SANE
Events such as these may be rare but do not come out of the blue. In both cases the red warning flags were flying yet no-one stepped in to prevent the tragedies occurring.
It is not an expensive revolution in care we need but common sense: you do not leave an 82-year-old mother alone to care for her mentally ill son whose medication has been radically changed, with no support and no-one to call.
Nor do you allow someone who may be becoming severely disturbed to dictate their own care and treatment without rigorous assessment of the risk they may pose to themselves or others.
We have had 15 years of independent inquiries all exposing the same fault lines in the care and treatment of people with serious mental illness.
We hear the same litany of failures to share information and involve carers and families, and we have the same unnecessary loss of life.