In 1972, Hudson [2] gave a method for the construction of pandiagonal magic squares of order 6t±1. In this paper we give the definition of pandiagonal Latin squares and the methods for the construction of self orthogonal pandiagonal Latin squares of order 4, 8, 9, 27 and prime p⩾5. One can use the technique of Kronecker products for the construction of self orthogonal pandiagonal Latin squares and pandiagonal magic squares of order n provided n ≠ 4t+2, 9t+3, 9t+6.