Denote by H n the cone of n-by- n positive semidefinite Hermitian matrices. Let d 2 be the generalized matrix function (or immanant) afforded by the symmetric group S n and the irreducible degree n − 1 character corresponding to the partition (2,1,…,1). Suppose A ∈ H n is partitioned into blocks, A= A 11 A 12 A ∗ 12 A 22 If n⩾4, then d 2(diag(A 11,A 22))⩾ d 2(A). This follows from the fact that d 2 is a Schur-concave function of the spectrum of A for A ∈ C n , where C n consists of the matrices in H n whose diagonal entries all equal 1.