Abstract
We consider a connected threshold graph G with A, S as its adjacency matrix and Seidel matrix respectively. In this paper several spectral properties of S are analysed. We compute the characteristic polynomial and determinant of S. A formula for the multiplicity of the Seidel eigenvalues ±1 and characterisation of threshold graphs with at most five distinct Seidel eigenvalues are derived. Finally it is shown that two non isomorphic threshold graphs may be cospectral for S.