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Round 4
5 July 1964
| Heidenfeld (3) |
(½-½) |
Cassidy (3) |
| Wilson (2½) |
(1-0) |
O'Hare (2) |
| Byrne (2) |
(1-0) |
Cunnane (2) |
| O'Riordan (2) |
(½-½) |
Lewis, W. (2) |
| Reilly (1½) |
(1-0) |
O'Kane (2) |
| Lewis, E. W. (1½) |
(½-½) |
Ireton (1½) |
| Ballance (1½) |
(1-0) |
Egan (1) |
| O'Leary (1) |
(½-½) |
Coll (1½) |
| Cox (1) |
(1-0) |
Doyle (1) |
| Ó Siochrú (½) |
(0-1) |
Collins (½) |
| Stewart (0) |
1 |
Bye |
Scores after round 4
| Cassidy | 3½ |
| Heidenfeld | 3½ |
| Wilson | 3½ |
| Byrne | 3 |
| Ballance | 2½ |
| Lewis, W. | 2½ |
| O'Riordan | 2½ |
| Reilly | 2½ |
| Coll | 2 |
| Cox | 2 |
| Cunnane | 2 |
| Ireton | 2 |
| Lewis, E. W. | 2 |
| O'Hare | 2 |
| O'Kane | 2 |
| Collins | 1½ |
| O'Leary | 1½ |
| Doyle | 1 |
| Egan | 1 |
| Stewart | 1 |
| Ó Siochrú | ½ |