  Choi Seok-Jeong studied Latin squares at least 60 years earlier than Euler
although this was less known. He introduced a pair of orthogonal Latin squares
of order 9 in his book. Interestingly, his two orthogonal non-double-diagonal
Latin squares produce a magic square of order 9, whose theoretical reason was
not studied. There have been a few studies on Choi's Latin squares of order 9.
The most recent one is Ko-Wei Lih's construction of Choi's Latin squares of
order 9 based on the two $3 \times 3$ orthogonal Latin squares.
  In this paper, we give a new generalization of Choi's orthogonal Latin
squares of order 9 to orthogonal Latin squares of size $n^2$ using the
Kronecker product including Lih's construction. We find a geometric description
of Choi's orthogonal Latin squares of order 9 using the dihedral group $D_8$.
We also give a new way to construct magic squares from two orthogonal
non-double-diagonal Latin squares, which explains why Choi's Latin squares
produce a magic square of order 9.
