A systematic development of discrete transparent boundary conditions (TBCs) for higher-order finite-difference approximations to Schrödinger-type equations is formulated and tested numerically. The finite-range interaction scheme for the original wave function is transformed into an equivalent nearest-neighbour coupling scheme for unit cells represented by multi-component spinors. This nearest-neighbour scheme lends itself to an established approach: the single-cell translation matrix for the extended spinor is constructed in Z space and cast into Jordan form. TBCs are obtained by setting out-bound growing spinor contributions equal to zero. Specifically we consider unitary extensions to the Crank–Nicolson time-propagation scheme for the time-dependent Schrödinger equation in (1+1)D. Numerical examples are given for selected higher-order propagation schemes. Finally, a simplified formulation based on a single, dominant growth factor is discussed and tested numerically.