It has been suggested that ice cores may preserve detectable enhancements of some terrestrially rare radioisotopes, 10Be, 26Al, 36Cl, resulting from a near-Earth core-collapse supernova(SN) [J. Ellis, B.D. Fields and D.N. Schramm, Astrophys. J. 470 (1996) 1227]. Both 10Be and 36Cl are also produced by atmospheric cosmic ray spallation and hence are influenced by processes that modulate the Earth's cosmic ray flux. Previous studies [G.M. Raisbeck, F. Yiou, D. Bourles, C. Lorius, J. Jouzel and N. I. Barkov, Nature 326 (1987) 273], [L.G. Thompson, T. Yao, M.E. Davis, K.A. Henderson, E. Mosley-Thompson, P.-N. Lin, J. Beer, H.-A. Synal, J. Cole-Dai and J.F. Bolzan, Science 276 (1997) 1821] have suggested that enhancements occurred in the 10Be and 36Cl fluxes at ∼35 ky and at ∼60 ky for 10Be. Thus we have searched for potential SN condensates with 26Al amongst grains filtered from the 308.6m Guliya ice core recovered from the Qinghai-Tibetan plateau in China [L.G. Thompson, T. Yao, M.E. Davis, K.A. Henderson, E. Mosley-Thompson, P.-N. Lin, J. Beer, H.-A. Synal, J. Cole-Dai and J.F. Bolzan, Science 276 (1997) 1821]. We searched for potential core-collapse SN condensate grains corundum (Al2O3), hibonite (CaAl12O19) and spinel (MgAl2O4) (see [D.S. Ebel and L. Grossman, Geochim. Cosmochim. Acta 65 (2001) 469]) in Guliya grain samples from the following time periods: ∼2−10 ky, ∼25−27 ky, ∼34−36 ky, ∼53−57 ky, ∼59−62 ky and ∼68−72 ky. These minerals are rare among terrestrial rocks and fine-grained atmospheric dust of terrestrial origin. Furthermore, they are insoluble in the acids employed in the sample preparation process and therefore separable from other minerals, such as silicates, that have high terrestrial abundances. Candidate SN condensate grains were identified among their terrestrial diluents employing a procedure developed at the University of Chicago for detecting presolar grains in meteoritic samples [S. Amari, R.S. Lewis and E. Anders, Geochim. Cosmochim. Acta 58 (1994) 459]. A set of 37 grains from the ∼34−36 ky, ∼53−57 ky and ∼59−62 ky samples were analyzed with the NanoSIMS at Washington University to measure their oxygen isotopic ratios. The preliminary results indicate that the analyzed grains, representing < 15% of those identified, do not possess the extreme O isotopic ratios expected to characterize a SN source [S. Amari and E. Zinner, Nucl. Phys. A 621 (1997) 99c], [T. Rauscher, A. Heger, R.D. Hoffman and S.E. Woosley, Astrophys. J. 576 (2002) 323].