In an earlier paper, [A.D. Keedwell, Australas J. Combin. 47 (2010), 227-238], we proved that complete sets of orthogonal diagonal Sudoku latin squares exist of all orders p 2 , where p is a prime. We also showed that complete sets of orthogonal Sudoku latin squares which are left semidiagonal exist of all orders p 2s , s > 1, and we conjectured that these may be right semi-diagonal also but we were not able to prove the latter result. In this note, we show that our conjecture regarding existence was correct.