Describe a straightforward recursive and global approach for the solution of rational interpolation problems. The derivation is based on a simple and well known matrix identity, namely, the Schur reduction procedure, and exploits connections with structured matrices. The authors use the interpolation data to construct a convenient structure and then apply a recursive triangularization procedure. This leads to a transmission-line cascade of first-order J-lossless sections that makes evident the interpolation property. State-space descriptions for each section and for the entire cascade are given.