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An integral relation is established between the Green functions correspondingto two Hamiltonians which are supersymmetric (SUSY) partners and in general maypossess both discrete and continuous spectra. It is shown that when thecontinuous spectrum is present the trace of the difference of the Greenfunctions for SUSY partners is a finite quantity which may or may not be equalto zero despite the divergence of the traces of each Green function. Ourfindings are illustrated by using the free particle example considered both onthe whole real line and on a half line

SUSY transformation of the Green function and a trace formula