  We make explicit the exponential bound on the degrees of the polynomials
appearing in the Effective Quillen-Suslin Theorem, and apply it jointly with
the Hilbert-Burch Theorem to show that the syzygy module of a sequence of m
polynomials in n variables defining a complete intersection ideal of grade two
is free, and that a basis of it can be computed with bounded degrees. In the
known cases, these bounds improve previous results.
