Discretizing the Dirac equation on a uniform grid with the central difference formula often generates spurious states. We propose a staggered-grid scheme in the framework of the finite-difference method that suppresses these spurious states without introducing Wilson terms or $\mathit{ad}$ hoc filtering. In this approach, the large and small components of the Dirac equation are placed on interlaced nodes, and the first-order derivatives are evaluated between staggered points, yielding a Hamiltonian that breaks the unitary transformation between $H_{\kappa }$ and $H_{-\kappa }$. Benchmarks with the nuclear Woods–Saxon potentials demonstrate one-to-one agreement with the eigenvalues obtained from the shooting method and the asymmetric finite-difference method, rapid convergence for weakly bound states, and reduced box-size sensitivity. The method retains the simplicity of central differences and standard matrix diagonalization, while naturally extending to higher-order and multidimension systems. It provides a compact and efficient tool for relativistic bound-state and scattering calculations.

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• Nuclear structure & decays
• Relativistic wave equations
• Nuclear many-body theory