An apparatus is used to cover a wall corner where lengths of cove base meet. One part is a wall adapter. It is composed of a right angle of thin material with one-half of a mechanical mating structure at its outer apex. The other part is a corner cover composed of a right angle of a thicker material with a narrower extent, but taller than the wall adapter. The cove base corner cover provides a unified junction between the two adjacent cove base sides of a corner. The corner cover is initially held correctly in place by being mechanically mated to the wall adapter. Corners may be inside or outside corners. Matings include snap fit, friction fit and a hanging tab and slot. These two types of covers might operate with a common wall adapter, but, of course, are of somewhat complementary shapes. Their right angles face in opposite orientations.