Spectral variation under congruence for a nonsingular matrix with 0 on the boundary of its field of values

In this paper we describe the possible spectra among matrices congruent to a given nonsingular matrix such that 0 is a boundary point of its field of values. In the process we give a reducible form under congruence for A. If A is either singular or such that 0 is not a boundary point of its field of values, the possible spectra among matrices congruent to Awere studied in [Linear and Multilinear Algebra 49 (2001) 243].