  In this paper, we describe a compact and practical algorithm to construct
Hermitian Young projection operators for irreducible representations of the
special unitary group SU(N), and discuss why ordinary Young projection
operators are unsuitable for physics applications. The proof of this
construction algorithm uses the iterative method described by Keppeler and
Sj\"odahl. We further show that Hermitian Young projection operators share
desirable properties with Young tableaux, namely a nested hierarchy when
"adding a particle". We end by exhibiting the enormous advantage of the
Hermitian Young projection operators constructed in this paper over those given
by Keppeler and Sj\"odahl.
