  We introduce the Z_2-extended Griess algebra of a vertex operator
superalgebra with an involution and derive the Matsuo-Norton trace formulae for
the extended Griess algebra based on conformal design structure. We illustrate
an application of our formulae by reformulating the one-to-one correspondence
between 2A-elements of the Baby-monster simple group and N=1 c=7/10 Virasoro
subalgebras inside the Baby-monster vertex operator superalgebra.
