Additions
| from | Name | Pos | Team | Team | ||
|---|---|---|---|---|---|---|
| 07/1959 |  | Echevarria | GK | |||
| 07/1959 | | Barrenechea | DF | |||
| 07/1959 | | Echeberría | DF | |||
| 07/1959 | | Esturo | DF |  | Athletic Club | Athletic |
| 07/1959 | | Iturriaga | MF | |||
| 07/1959 | | Chechu | FW | |||
| 07/1959 | | Molinuevo | MA |
Departures
| from | Name | Pos | Team | Team | ||
|---|---|---|---|---|---|---|
| 07/1959 | | Olivares | GK |  | CA Osasuna | Osasuna |
| 07/1959 | | Rodríguez López | DF |  | Rayo Vallecano | Rayo |
| 07/1959 | | Urquijo | FW | | Athletic Club | Athletic |