Visual appearance can be phenomenologically modeled through an integral equation, known as reflectance equation. It describes the surface radiance which depends on the interaction between incident light field and surface Bidirectional Reflectance Distribution Function (BRDF). Being defined on the Cartesian product of the incident and outgoing hemispheres, hemispherical basis is the natural way to represent surface BRDFs. Nonetheless, due to their compactness in the frequency space, spherical harmonics have been extensively used for this purpose. Addressing the geometrical compliance of hemispherical basis, this paper proposes a Cartesian product of the hemispherical harmonics to provide a compact representation of plausible BRDFs, while satisfying the Helmholtz reciprocity property. We provide an analytical analysis and experimental justification that our basis provides better approximation accuracy when compared to similar bases in literature.