A Fuchsian system is a linear system of ordinary differential equations on Riemann’s sphere having only logarithmic poles. When the conjugacy classes of the tuple of matrices-residua (resp. of monodromy operators) define the tuple up to conjugacy, the former is said to be rigid. In the rigid case the author provides a concrete relation between Katz’s middle convolution and Yokoyama’s extension and shows the equivalence of these operations. In this context he mentions results of Dettweiler and Reiter, Crawley-Boevey, Haraoka, Kostov, Oshima and the Okubo normal form for Fuchsian systems.