The current rate of inmates taking their own lives at the Acklington jail was confirmed in data published by the Ministry of Justice.
During the course of 2017, one person killed themselves at the male-only Category C unit, which was privatised at the end of 2013 and is run by Sodexo Justice Services.
This was compared to three people committing suicide in 2016 – the highest in four years, compared to one suicide in each of 2015, 2014 and 2013.
A further four people died in custody at HMP Northumberland in 2017.
Nationally, the figures show that 295 people died in jails last year, including 70 people who lost their lives through suicide.
This represents a drop in suicide rates, compared to 120 in 2016, which was the highest on record.
However, violence and self-injury have reached record levels, with the Howard League for Penal Reform blaming overcrowding in prisons.
The figures show that there were 28,165 assaults in jails in England and Wales in 12 months to the end of September 2017, a 12 per cent rise on the previous year.
They included 7,828 assaults on prison staff – a 22 per cent rise compared to the previous 12 months.
Incidents of self-injury increased by 12 per cent to 42,837 over the same period.
It means that the number of assaults and self-injuries are at their highest since current recording practices began in 1978.