Let \((G,B,N)\) be a group with an irreducible spherical BN-pair of rank at least \(2\), and let \(U\) be a nilpotent normal subgroup of \(B\) with \(B=U(B\cap N)\). The authors show that \(U\) is uniquely determined in this situation. As a consequence, they obtain a complete description of all irreducible spherical split BN-pairs of rank at least \(2\).