We have solved exactly the two-component Dirac equation in the presence of a spatially one-dimensional Hulthen potential, and presented the Dirac spinors of scattering states in terms of hypergeometric functions. We have calculated the reflection and
transmission coefficients by the matching conditions on the wavefunctions, and investigated the condition for the existence of transmission resonances. Furthermore, we have demonstrated how the transmission-resonance condition depends on the shape of the potential.
