Latin squares with a unique intercalate

Suppose that n=1 or 5 mod 6 and n≥7. We construct a Latin square Ln of order n with the following properties: Hence Ln generalises the square that Sade famously found to complete Norton's enumeration of Latin squares of order 7. In particular, Ln is what is known as a self-switching Latin square and possesses a near-autoparatopism.