According to a press release from the California Department of Corrections and Rehabilitation, 75-year-old Joseph S. Cordova was found unresponsive in his single cell on July 1 at 4:08 p.m.
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Officials say medical assistance was rendered, an ambulance was called but Cordova was pronounced dead at 4:22 p.m.
His cause of death and COVID-19 status will be determined by the Marin County Coroner.
Cordova had been on row since 2007 for the 1979 rape and murder of eight-year-old Cannie Melinda Bullock in San Pablo.
Last week, a 71-year-old man also on San Quentin's death row, tested positive for the coronavirus after he was found unresponsive in his cell.
It's the first known coronavirus death inside San Quentin.
RELATED: Marin health official expects COVID-19 outbreak at San Quentin Prison to double in next 10 days
Nearly a third of inmates at San Quentin prison, more than 1,100 people, have tested positive for COVID-19.
During a state hearing about the crisis, state lawmakers said moving inmates from San Quentin to the California Correctional Center in Susanville has led to an outbreak at that prison.
The San Francisco Public defender's office is now working with certain inmates considered low risk to get them released.