As shown in §G.13.3, an FDN feedback matrix is lossless if and only if its eigenvalues have modulus 1 and its eigenvectors are linearly independent.
A unitary matrix is any (complex) matrix that is inverted by its own (conjugate) transpose:
All unitary (and orthogonal) matrices have unit-modulus eigenvalues and linearly independent eigenvectors. As a result, when used as a feedback matrix in an FDN, the resulting FDN will be lossless.