The lowest-energy structure of thiolate-group-protected Au-38 (SR)(24) is with ab initio computations. A unique bi-isocahedral Au-23 core is predicted for the Au-38(SR)(24) cluster, consistent with recent experimental and theoretical confirmation of the icosahedral Au-13 core for the [Au-25(SR)(18)](-) cluster. The computed optical absorption spectrum and X-ray diffraction pattern are in good agreement with experimental measurements. Like the "magic-number cluster [Au-25(SR)(18)](-), the high stability and selectivity of the magic-number Au-38(SR)(24) cluster is attributed to high structural compatibility between the bi-isocahedral Au-23 core and the 18 exterior staple motifs.