Sample spectra of candidate members of the Lupus star forming region whose membership is ruled out by our new observations. The spectra presented here correspond to the coolest non-members having M0 or later spectral types. The prominent CaII triplet absorption lines at 8498 Å, 8542 Å and 8662 Å are clear indicators of very low surface gravities indicating that the stars are actually giants. Giant stars in our sample earlier than M0, not shown here, are also identified through strong CaII absorption. The CaII lines in absorption disappear at mid-M types, but other surface gravity indicators discussed in the text clearly show that the bottom four stars are giants as well.