  We study finite systems of subspaces of a complex Hilbert space such that
each pair of subspaces satisfies a certain condition as described in the
following. For each subspace excepting the first one an angle between this
subspace and the first one is fixed. The set of all subspaces excluding the
first one is divided into disjoint subsets. Each such subset consists of one or
two subspaces. Subspaces from different subsets are orthogonal and orthogonal
projections onto subspaces from the same subset commute.
