Abstract: Transmission, reflection and fission of an internal solitarywave incident upon a step in a two-layer fluid system are investigatedanalytically based on the matched-asymptotic expansion andthe Green function. The reduced boundary condition relevant to the effect ofthe step-topography on Boussinesq equations is derived by applying theconformal mapping theory and solving the singular Fredholm integralequation. A problem of the `initial' value for KdV evolution equation isformulated. The explicit expressions for transmitted and reflected waves aregiven by the inverse scattering method. It follows that there exist obviouseffects of step height, density ratio and thickness ratio of upper- tolower-layer on the amplitudes of transmitted and reflected waves and theirnumber of fission. It is also found that when the upper layerthickness is larger than the lower layer one, the amplitude of the reflectedwave monotonously increases with theincrease of step height is before the critical point, thenmonotonously decreases, and it is the other way round for thetransmitted wave. The phase of the reflected wave on the convex step isjust opposite to the incident wave, and its maximum amplitude can approachseveral folds of the incident one. The reflected wave on the concave step can evolveinto a single solitary wave in certain stratified situations, which differfrom the oscillating decay tail in the single layer fluid system.