The copositive completion problem: Unspecified diagonal entries

In [L. Hogben, C.R. Johnson, R. Reams, The copositive matrix completion problem, Linear Algebra Appl. 408 (2005) 207–211] it was shown that any partial (strictly) copositive matrix all of whose diagonal entries are specified can be completed to a (strictly) copositive matrix. In this note we show that every partial strictly copositive matrix (possibly with unspecified diagonal entries) can be completed to a strictly copositive matrix, but there is an example of a partial copositive matrix with an unspecified diagonal entry that cannot be completed to a copositive matrix.