  We establish an Excision type theorem for niceness of group structure on the
orbit space of unimodular rows of length $n$ modulo elementary action. This
permits us to establish niceness for relative versions of results for the cases
when $n = d+1$, $d$ being the dimension of the base algebra. We then study and
establish niceness for the case when $n = d$, and also establish a relative
version, when the base ring is a smooth affine algebra over an algebraically
closed field.
