It is generally believed that at-Γ bound states in the continuum (BICs) are enclosed by a linearly polarized vortex in momentum space when the structures have mirror (σz) symmetry, in-plane inversion (I) symmetry, and time reversal symmetry (T). Here, we reveal an anomalous situation in which at-Γ BICs can be enclosed by linearly and elliptically polarized far-field even when the σz, I, and T symmetries are all maintained in non-Bravais lattices, which is radically different from previous cognition. Asymmetric, diatomic structures are designed to elaborate this intriguing phenomenon. By controlling the geometric parameters or refractive indexes of the two meta-atoms, the far-field polarization around the at-Γ BICs gradually deviates from linear polarization and approaches circular polarization. Our findings reveal that non-Bravais lattices can provide a novel platform to manipulate the far-field polarization, showing important applications in quantum entanglement, structured light, and radiation modulation.