  We address the existence of global solutions to the initial value problem for
the integrable nonlocal derivative nonlinear Schr\"{o}dinger equation in
weighted Sobolev space $H^{2}(\mathbb{R})\cap H^{1,1}(\mathbb{R})$. The key to
prove this result is to establish a bijectivity between potential and
reflection coefficient by using the inverse scattering transform method in the
form of the Riemann-Hilbert problem.
