A screen cylinder or plate has a screening surface and accepts surface on opposite faces, and screens pulp flowing in a flow direction to separate accepts from rejects. A number of substantially parallel macro grooves are formed in the screening surface generally transverse to the flow direction, and a number of parallel micro grooves are formed in the screening surface within each macro groove also generally transverse to the flow direction. The macro grooves induce shear stress in the reject material flowing in the flow direction to keep it in constant motion and to prevent it from forming a mat on the screening surface. The micro grooves induce micro turbulence into the pulp at the immediate area of screening openings extending from each micro groove to the accepts surface, to fluidize the pulp so that accepts readily pass through the screening openings toward the accepts surface. Each micro groove within a macro groove is located further away from the accepts surface moving in the flow direction. The contour of each micro groove preferably includes a slightly slanted upstream wall, a sloped downstream wall, and a depression between the upstream and downstream walls. The depression may include a substantially flat surface, or be a continuation of the downstream wall; the slots or holes forming the screening openings are provided in the depression. It is possible to screen with a rejects rate of about 3-10% at debris removal efficiency of above about 85%.