A Latin square of size n is an arrangement of n symbols in an n-by-n square in such a way that each row and column has each symbol appearing exactly once.

A randomised Latin square generates random configurations of the symbols for any given n.

Example n=4 randomised Latin square

0 2 3 1
2 1 0 3
3 0 1 2
1 3 2 0
Task

 Create a function/routine/procedure/method/... that given n generates a randomised Latin square of size n.
 Use the function to generate and show here, two randomly generated squares of size 5.
Note
 
Strict Uniformity in the random generation is a hard problem and not a requirement of the task.

Reference

 Wikipedia: Latin square
 OEIS: A002860


Clear[RandomLatinSquare]
RandomLatinSquare[n_] := Module[{out, ord},
  out = Table[RotateLeft[Range[n], i], {i, n}];
  out = RandomSample[out];
  ord = RandomSample[Range[n]];
  out = out[[All, ord]];
  out
  ]
RandomLatinSquare[5] // Grid