| 1º Turno | 2º Turno | 3º Turno | Final |
Round:
Played
10/03/1959 - Saturday
América-RN
3
x
2
Santa Cruz de Natal-RN
10/04/1959 - Sunday
ABC-RN
5
x
0
Atlético-RN
10/07/1959 - Wednesday
Riachuelo-RN
5
x
0
Alecrim-RN
10/11/1959 - Sunday
Santa Cruz de Natal-RN
0
x
1
ABC-RN
10/14/1959 - Wednesday
Alecrim-RN
0
x
7
América-RN
10/18/1959 - Sunday
Riachuelo-RN
2
x
0
Atlético-RN
10/21/1959 - Wednesday
Alecrim-RN
2
x
2
ABC-RN
10/25/1959 - Sunday
América-RN
2
x
2
Riachuelo-RN
10/28/1959 - Wednesday
Atlético-RN
0
x
2
Santa Cruz de Natal-RN
11/01/1959 - Sunday
ABC-RN
2
x
1
Riachuelo-RN
11/04/1959 - Wednesday
Atlético-RN
0
x
1
América-RN
11/08/1959 - Sunday
Santa Cruz de Natal-RN
2
x
1
Alecrim-RN
11/11/1959 - Wednesday
ABC-RN
4
x
1
América-RN
11/14/1959 - Saturday
Atlético-RN
0
x
3
Alecrim-RN
11/15/1959 - Sunday
Riachuelo-RN
1
x
1
Santa Cruz de Natal-RN