  Let X be a smooth variety over a field k and D an effective divisor whose
support has simple normal crossings. We construct an explicit cycle map from
the r-th Nisnevich motivic complex of the pair (X,D) to a shift of the r-th
relative Milnor K-sheaf of (X,D). We show that this map induces an isomorphism
for all i greater or equal the dimension of X between the motivic Nisnevich
cohomology of (X,D) in bidegree (i+r,r) and the i-th Nisnevich cohomology of
the r-th relative Minor K-sheaf of (X,D). This generalizes the well-known
isomorphism in the case D=0. We use this to prove a certain Zariski descent
property for the motivic cohomology of the pair (\A^1_k, (m+1){0}).
