  This paper deals with the problem of multi-degree reduction of a composite
B\'ezier curve with the parametric continuity constraints at the endpoints of
the segments. We present a novel method which is based on the idea of using
constrained dual Bernstein polynomials to compute the control points of the
reduced composite curve. In contrast to other methods, ours minimizes the
$L_2$-error for the whole composite curve instead of minimizing the
$L_2$-errors for each segment separately. As a result, an additional
optimization is possible. Examples show that the new method gives much better
results than multiple application of the degree reduction of a single B\'ezier
curve.
