10 teams on 4 courts in 11 games?

[Paulepin]

I am trying to setup a round-robin for 10 teams on only 4 (not 5) courts. This means two teams will not play in each round (due to the lack of a fifth court).  I need these two teams to play each other in the next round so that a cold team (one that sits out) doesn't play a hot team (one that's just played) in any round.  There will be 45 games in total, which means 11 rounds of 4 games and 1 round of 1 game.  We can fit the one game into a fifth court once but otherwise that court is needed for other competitions.  The cold versus cold requirement is making this more complicated to work out.  Can anyone help?  This is the best I've been able to manage:

[Ian Wakeling]

I have found the 12 round schedule below by computer search and I think it should work.  You have the option of shortening the tournament by playing (9 v 10) on the 5th court in round 11.

  C1      C2      C3      C4       byes
 (1  9)  (2  6)  (3 10)  (4  5)    (7  8)
 (1  5)  (2  3)  (6 10)  (7  8)    (4  9)
 (1 10)  (2  5)  (3  8)  (4  9)    (6  7)
 (1  8)  (2  4)  (5 10)  (6  7)    (3  9)
 (1  7)  (2  8)  (3  9)  (4 10)    (5  6)
 (1  3)  (2  9)  (4  7)  (5  6)    (8 10)
 (3  4)  (5  7)  (6  9)  (8 10)    (1  2)
 (1  2)  (4  6)  (7 10)  (8  9)    (3  5)
 (1  6)  (3  5)  (4  8)  (7  9)    (2 10)
 (2 10)  (3  7)  (5  9)  (6  8)    (1  4)
 (1  4)  (2  7)  (3  6)  (5  8)    (9 10)
 (9 10)