In this paper propagation of transient electromagnetic waves in a reciprocal bi-isotropic medium is presented. The constitutive relations are convolution integrals with two susceptibility kernels that model the medium. The propagation problem is solved by the introduction of a wave-splitting technique. This wave-splitting is used to solve the propagation problem using either an imbedding approach or a Green's function technique. In particular, the scattering problem of an electromagnetic wave that impinges normally on a slab of finite or infinite extent is solved. The slab is assumed to be inhomogeneous with respect to depth. The scattering problem consists of finding the reflected and the transmitted fields and the generic quantities are the reflection and the transmission kernels of the medium. Explicit expressions for the rotation and the attenuation of the wave front is presented for the inhomogeneous slab. In the special case of a homogeneous infinite slab it is proved that the reflection kernel satisfies a nonlinear Volterra equation of the second kind, very suitable for numerical calculations. It is also proved that no cross polarization contribution appears for the homogeneous slab. Several numerical computations illustrate the analysis.