  A time-variant analogue of an interpolation problem equivalent to the relaxed
commutant lifting problem is introduced and studied. In a somewhat less general
form the problem already appears in the analysis of the set of all solutions to
the three chain completion problem. The interpolants are upper triangular
operator matrices of which the columns induce contractive operators. The set of
all solutions of the problem is described explicitly. The results presented are
time-variant analogues of the main theorems in [A.E. Frazho, S. ter Horst, and
M.A. Kaashoek, All solutions to the relaxed commutant lifting problem, Acta
Sci. Math. (Szeged) 72 (2006), 299--318].
