The existence of anisotropy in paramagnetic cubic crystals has never been observed and it was only vaguely conjectured by Schlapp and Penney in 1932 for chrome alums. In this paper, a calculation based on P. R. Weiss's theory (1948) shows that the paramagnetic anisotropy does exist in the single crystals of chrome alums. Percentage differences (γ ) between the susceptibility along direction (χ) and that along direction (χ) in KCr alum single crystal at room temperature are given for several values of magnetic field. It is pointed out that the ordinary concept of principal susceptibilities along respectively three mutually perpendicular magnetic axes is no longer applicable to describe the paramagnetic anisotropy of the cubic crystals of chrome alums.