At first glance, season 1963/64 was another dreadful season for Celtic, and there is no real point in denying that. Rangers won a treble in Scotland, and beat Celtic five times 3-0, 3-0, 2-1, 1-0 and 2-0. Celtic had a major complex about Rangers… Let us talk about this aspect first. The end of season
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 | 2 - 1 |  |
Celtic Celtic Park Glasgow | Sturm Graz |
 | v | |
Hearts Tynecastle Park Europe | Celtic |
| Team | P | W | D | L | F | A | GD | Pts | |
|---|---|---|---|---|---|---|---|---|---|
| 1 | Hearts | 8 | 7 | 1 | 0 | 19 | 6 | 13 | 22 |
| 2 | Celtic | 8 | 5 | 2 | 1 | 11 | 5 | 6 | 17 |
| 3 | Hibernian | 8 | 2 | 5 | 1 | 14 | 10 | 4 | 11 |
| 4 | Dundee United | 8 | 2 | 4 | 2 | 14 | 13 | 1 | 10 |
| 5 | Kilmarnock | 8 | 2 | 4 | 2 | 11 | 11 | 0 | 10 |
| 6 | Rangers | 8 | 1 | 6 | 1 | 8 | 9 | -1 | 9 |
| 7 | St Mirren | 8 | 2 | 3 | 3 | 5 | 7 | -2 | 9 |
| 8 | Falkirk | 8 | 2 | 3 | 3 | 10 | 14 | -4 | 9 |
| 9 | Dundee | 9 | 2 | 3 | 4 | 8 | 13 | -5 | 9 |
| 10 | Motherwell | 8 | 1 | 5 | 2 | 12 | 12 | 0 | 8 |
| 11 | Aberdeen | 8 | 2 | 1 | 5 | 5 | 9 | -4 | 7 |
| 12 | Livingston | 9 | 1 | 3 | 5 | 10 | 18 | -8 | 6 |
