  To a Seifert matrix of a knot K one can associate a matrix w(K) with entries
in the rational function field, Q(t). The Murasugi, Milnor, and Levine-Tristram
knot signatures, all of which provide bounds on the 4-genus of a knot, are
determined by w(K). More generally, the minimal rank of a representative of the
class represented by w(K) in the Witt group of hermitian forms over Q(t)
provides a lower bound for the 4-genus of K. Here we describe an easily
computed new bound on the minimal rank of the class represented by w(K).
Furthermore, this lower bound is complete modulo torsion in the Witt group.
Specifically, if the bound on the rank is M, then 4w(K) has a representative of
rank exactly 4M. Applications to explicit knots are given, finding 4-genus
bounds for specific knots that are unattainable via other approaches.
