The non-axial reflection-asymmetric β32 shape in some transfermium nuclei with N = 150, namely 246 Cm, 248 Cf, 250 Fm, and 252 No are investigated with multidimensional constrained covariant density functional theories. By using the density-dependent point coupling covariant density functional theory with the parameter set DD-PC1 in the particle-hole channel, it is found that, for the ground states of 248 Cf and 250 Fm, the non-axial octupole deformation parameter β32 > 0.03 and the energy gain due to the β32 distortion is larger than 300 keV. In 246 Cm and 252 No, shallow β32 minima are found. The occurrence of the non-axial octupole β32 correlations is mainly from a pair of neutron orbitals [734]9/2 (νj 15/2 ) and [622]5/2 (νg 9/2 ) which are close to the neutron Fermi surface and a pair of proton orbitals [521]3/2 (πf 7/2 ) and [633]7/2 (πi 13/2 ) which are close to the proton Fermi surface. The dependence of the non-axial octupole effects on the form of energy density functional and on the parameter set is also studied.PACS numbers: 21.10. Dr, 21.60.Jz, 27.90.+b The majority of observed nuclear shapes is of spheroidal form which is usually described by β 20 . The existence of the nonaxial-quadrupole (triaxial) deformation β 22 [1-3] and the axial octupole deformation β 30 [4] in atomic nuclei have also been confirmed both experimentally and theoretically. However, there is no a priori reason to neglect the nonaxial-octupole deformations, especially the β 32 deformation [5][6][7]. The pure β 32 deformation has a tetrahedral symmetry with a symmetry group T D d . The existence of non-trivial irreducible representations of this group makes it possible for a nuclei to have large energy gaps in their single-particle levels, thus increasing it's stability [8]. It has been anticipated that β 32 deformation occurs in the ground states of some nuclei with special combinations of the neutron and proton numbers [7][8][9]. Recently, lots of theoretical studies focus on this nuclear shape, either from the T D d -symmetric single particle spectra [7,[9][10][11] or from various nuclear models including the macroscopicmicroscopic model [9,[11][12][13], the Skyrme Hartree-Fock (SHF), SHF+BCS, or Skyrme Hartree-Fock-Bogoliubov models [11][12][13][14][15][16][17][18], and the Reflection Asymmetric Shell Model (RASM) [19,20]. In particular, Dudek et al. predicted that a negative-parity band in 156 Gd is a favorable candidate to manifest tetrahedral symmetry [13] which has stimulated several interesting experimental studies [21,22].Nowadays the study of nuclei with Z ∼ 100 becomes more and more important because it not only reveals the structure of these nuclei themselves but also provides significant information for superheavy nuclei [23][24][25][26]. One of the relevant and interesting topics is how to explain the * sgzhou@itp.ac.cn low-lying 2 − states in some N = 150 even-even nuclei. In these nuclei, the bandhead energy E(2 − ) of the lowest 2 − bands is very low [27]. It is well accepted that the octupole correlation...