  The unified transform method is used to analyze the initial-boundary value
problem for the coupled derivative nonlinear Schr\"odinger(CDNLS) equations on
the half-line. In this paper, we assume that the solution $u(x,t)$ and $v(x,t)$
of CDNLS equations are exists, and we show that it can be expressed in terms of
the unique solution of a matrix Riemann-Hilbert problem formulated in the plane
of the complex spectral parameter $\lambda$.
