A cheapest stable nonconforming finite element method is presented for solving the incompressible flow in a square cavity without smoothing the corner singularities. The stable cheapest nonconforming finite element pair based on P₁×P₀ on rectangular meshes [29] is employed with a minimal modification of the discontinuous Dirichlet data on the top boundary, where $\widetilde{\mathcal{P}^h_0}$ is the finite element space of piecewise constant pressures with the globally one-dimensional checker-board pattern subspace eliminated. The proposed Stokes elements have the least number of degrees of freedom compared to those of known stable Stokes elements. Three accuracy indications for our elements are analyzed and numerically verified. Also, various numerous computational results obtained by using our proposed element show excellent accuracy.