We report a kind of two-dimensional (2D) electroconvection (EC) domain observed in a negative dielectric anisotropy nematic liquid crystal (LC) in a parallel-rubbed alignment cell. The domain is excited by an ac electric field with ultralow frequency, and can be transformed into a one-dimensional (1D) EC domain at low amplitude electric fields. We conclude that the 1D domain is a kind of Williams domain, while the 2D domain is induced by flexoelectric effect, the corresponding 2D texture coming from superposition of two sets of symmetrical 1D stripes oblique to the initial LC orientation.