| 1º Turno | 2º Turno | 3º Turno | Final |
Round:
Played
05/24/1959 - Sunday
Atlético-RN
2
x
2
Alecrim-RN
05/28/1959 - Thursday
América-RN
4
x
1
Riachuelo-RN
05/31/1959 - Sunday
Santa Cruz de Natal-RN
1
x
2
ABC-RN
06/03/1959 - Wednesday
Alecrim-RN
4
x
3
América-RN
06/07/1959 - Sunday
Riachuelo-RN
2
x
1
Santa Cruz de Natal-RN
06/10/1959 - Wednesday
ABC-RN
5
x
0
Atlético-RN
06/14/1959 - Sunday
Santa Cruz de Natal-RN
5
x
1
Alecrim-RN
06/21/1959 - Sunday
Atlético-RN
0
x
2
América-RN
06/28/1959 - Sunday
ABC-RN
0
x
1
Riachuelo-RN
07/01/1959 - Wednesday
América-RN
4
x
0
Santa Cruz de Natal-RN
07/05/1959 - Sunday
Riachuelo-RN
5
x
1
Atlético-RN
07/08/1959 - Wednesday
Alecrim-RN
0
x
2
ABC-RN
07/12/1959 - Sunday
Atlético-RN
1
x
3
Santa Cruz de Natal-RN
07/15/1959 - Wednesday
Riachuelo-RN
0
x
0
Alecrim-RN
07/19/1959 - Sunday
ABC-RN
1
x
2
América-RN