The role of conical intersections in the internal conversion (S-1 --> S-0) of photoexcited ketene (H2CCO) is analyzed. The energy-minimized projection of a portion of the S-1((1)A ")-S-0((1)A') seam of the conical intersection near the minimum energy-crossing point is studied as a function of the key internal coordinates R(C-C) and angle CCO. The characteristic parameters of the conical intersection points are used, to identify the two modes that evince the conical nature of the intersection, to determine the energy and singular part of the derivative coupling near the conical intersection, and to construct a transformation to diabatic states that rigorously removes the singularity in the derivative coupling. From the Franck-Condon region of the S-0 --> S-1 excitation, barrierless paths were identified on S-1 leading to R-e((A) over tilde(1)A "), the equilibrium geometry of S-1 ketene, and to R-mex, the minimum energy point on the S-1 --> S-0 seam of conical intersection. Following internal conversion onto S-0 near R-mex, the barrierless paths leading to R-e((X) over tilde(1)A(1)), the equilibrium geometry of ground-state ketene, were found.