  We study the relative position of four subspaces in a Hilbert space. For any
positive integer n, we give an example of exotic indecomposable system of four
subspaces in a Hilbert space whose defect is (2n+1)/3. By an exotic system, we
mean a system which is not isomorphic to any closed operator system under any
permutation of subspaces. We construct the examples by a help of certain nice
sequences used by Jiang and Wang in their study of strongly irreducible
operators.
