In a multiattribute relation or, equivalently, a multicolumn table a certain collection of the projections can be shown to be independent in much the same way as the factors in a Cartesian product or orthogonal components of a vector. A precise notion of independence for relations is defined and studied. The main result states that the operator which reconstructs the original relation from its independent components is the natural join, and that independent components split the full family of functional dependencies into corresponding component families. These give an easy-to-check criterion for independence. © 1977, ACM. All rights reserved. © 1977, ACM. All rights reserved.