Some of the schedules here stretch back over 7 or 8 years and I am not sure myself what's here sometimes! For what it's worth I don't remember anything like this.
For 36 players there are 630 player pairs, and a single round of 12 games contains 36 of those pairs. It is possible to have a schedule with the maximum possible of 17 rounds of play and no repeated pairs. Note that 18 rounds x 36 pairs would be in excess of 630, in which case there must be repeats.
(5 14 2) (6 33 4) (22 11 18) (24 36 7) (26 19 25) (27 1 32) (28 10 30) (3 9 13) (21 8 29) (31 15 16) (34 12 20) (23 35 17)
(6 15 3) (7 34 5) (23 12 19) (25 36 8) (27 20 26) (28 2 33) (29 11 31) (4 10 14) (22 9 30) (32 16 17) (18 13 21) (24 35 1)
(7 16 4) (8 18 6) (24 13 20) (26 36 9) (28 21 27) (29 3 34) (30 12 32) (5 11 15) (23 10 31) (33 17 1) (19 14 22) (25 35 2)
(8 17 5) (9 19 7) (25 14 21) (27 36 10) (29 22 28) (30 4 18) (31 13 33) (6 12 16) (24 11 32) (34 1 2) (20 15 23) (26 35 3)
(9 1 6) (10 20 8) (26 15 22) (28 36 11) (30 23 29) (31 5 19) (32 14 34) (7 13 17) (25 12 33) (18 2 3) (21 16 24) (27 35 4)
(10 2 7) (11 21 9) (27 16 23) (29 36 12) (31 24 30) (32 6 20) (33 15 18) (8 14 1) (26 13 34) (19 3 4) (22 17 25) (28 35 5)
(11 3 8) (12 22 10) (28 17 24) (30 36 13) (32 25 31) (33 7 21) (34 16 19) (9 15 2) (27 14 18) (20 4 5) (23 1 26) (29 35 6)
(12 4 9) (13 23 11) (29 1 25) (31 36 14) (33 26 32) (34 8 22) (18 17 20) (10 16 3) (28 15 19) (21 5 6) (24 2 27) (30 35 7)
(13 5 10) (14 24 12) (30 2 26) (32 36 15) (34 27 33) (18 9 23) (19 1 21) (11 17 4) (29 16 20) (22 6 7) (25 3 28) (31 35 8)
(14 6 11) (15 25 13) (31 3 27) (33 36 16) (18 28 34) (19 10 24) (20 2 22) (12 1 5) (30 17 21) (23 7 8) (26 4 29) (32 35 9)
(15 7 12) (16 26 14) (32 4 28) (34 36 17) (19 29 18) (20 11 25) (21 3 23) (13 2 6) (31 1 22) (24 8 9) (27 5 30) (33 35 10)
(16 8 13) (17 27 15) (33 5 29) (18 36 1) (20 30 19) (21 12 26) (22 4 24) (14 3 7) (32 2 23) (25 9 10) (28 6 31) (34 35 11)
(17 9 14) (1 28 16) (34 6 30) (19 36 2) (21 31 20) (22 13 27) (23 5 25) (15 4 8) (33 3 24) (26 10 11) (29 7 32) (18 35 12)
(1 10 15) (2 29 17) (18 7 31) (20 36 3) (22 32 21) (23 14 28) (24 6 26) (16 5 9) (34 4 25) (27 11 12) (30 8 33) (19 35 13)
(2 11 16) (3 30 1) (19 8 32) (21 36 4) (23 33 22) (24 15 29) (25 7 27) (17 6 10) (18 5 26) (28 12 13) (31 9 34) (20 35 14)
(3 12 17) (4 31 2) (20 9 33) (22 36 5) (24 34 23) (25 16 30) (26 8 28) (1 7 11) (19 6 27) (29 13 14) (32 10 18) (21 35 15)
(4 13 1) (5 32 3) (21 10 34) (23 36 6) (25 18 24) (26 17 31) (27 9 29) (2 8 12) (20 7 28) (30 14 15) (33 11 19) (22 35 16)
Above the pairs that do not occur are:
1 20
2 21
3 22
4 23
5 24
6 25
7 26
8 27
9 28
10 29
11 30
12 31
13 32
14 33
15 34
16 18
17 19
35 36
Finally note that player 35 and 36 always occur in the same column, so you may want to randomize the order of play within rounds.
Hope that helps.
