To deal with the vagueness and granularity in information systems, researchers proposed several methods such as fuzzy theory and rough set theory. This paper studies a class of covering-based generalized rough sets. In this setting, a covering can generate a lower approximation operation and an upper approximation operation, but some of common properties of classical lower and upper approximation operations are no longer satisfied. We investigate conditions for a covering under which these properties hold for the second type of covering-based lower and upper approximation operations.