<正> Let Fq2 be a finite field with q2 elements, where q is a power of a prime and let a→a=aq (1) be the involutive automorphism of Fq2 with the fixed field Fq. An n×n matrix H over Fq2 is said to be Hermitian, if HT=H, where H is the matrix obtained from H by replacing every dement of H by its image under