  A unit spherical Euclidean distance matrix (EDM) D is a matrix whose entries
can be realized as the interpoint (squared) Euclidean distances of n points on
a unit sphere. In this paper, given such a D and 1 \leq k < l \leq n, we
present a characterization of the set of all unit spherical EDMs whose entries
agree with those of D except possibly with the entry in the klth and lkth
positions. As a result, we show that this set can be discrete, consisting of
one or two elements, or it can be continuous. The results are derived using two
alternative approaches, the second of which is based on Cayley-Menger matrices.
