| 12. Round | 06/12/1959 | CA Osasuna | - | Athletic Club | 1:4 | ||||
| 13. Round | 13/12/1959 | Athletic Club | - | Atlético Madrid | 5:2 | ||||
| 14. Round | 20/12/1959 | Sevilla FC | - | Athletic Club | 5:0 | ||||
| 15. Round | 27/12/1959 | Athletic Club | - | Real Oviedo | 6:0 | ||||
| 16. Round | 03/01/1960 | Athletic Club | - | FC Barcelona | 4:1 | ||||
| 17. Round | 10/01/1960 | Real Valladolid | - | Athletic Club | 2:2 | ||||
| 18. Round | 17/01/1960 | Athletic Club | - | Granada CF | 3:0 | ||||
| 19. Round | 24/01/1960 | Real Sociedad | - | Athletic Club | 1:3 | ||||
| 20. Round | 31/01/1960 | Athletic Club | - | Real Madrid | 1:3 |
Spain