The double red clump (RC) observed in color-magnitude diagrams of the Milky Way bulge is at the heart of the current debate on the structure and formation origin of the bulge. This feature can be explained by the difference between the two RCs either in distance ("X-shaped scenario") or in chemical composition ("multiple-population scenario"). Here we report our high- resolution spectroscopy for the RC and red giant branch stars in a high-latitude field (b~-8.5{deg}) of the bulge. We find a difference in [Fe/H] between the stars in the bright and faint RC regimes, in the sense that the bright stars are enhanced in [Fe/H] with respect to the faint stars by 0.149{+/-}0.036dex. The stars on the bright RC are also enhanced in [Na/Fe] but appear to be depleted in [Al/Fe] and [O/Fe], although more observations are required to confirm the significance of these differences. Interestingly, these chemical patterns are similar to those observed among multiple stellar populations in the metal-rich bulge globular cluster Terzan 5. In addition, we find a number of Na-rich stars, which would corroborate the presence of multiple populations in the bulge. Our results support an origin of the double RC from dissolved globular clusters that harbor multiple stellar populations. Thus, our study suggests that a substantial fraction of the outer bulge stars would have originated from the assembly of such stellar systems in the early phase of the Milky Way formation.