  We examine Killing spinor equations of the general IIB pp-wave backgrounds,
which contain a scalar H(x^m,x^-) in the metric and a self-dual four-form
\xi(x^m,x^-) in the self-dual five-form flux. Considering non-harmonic extra
Killing spinors, we find that if the backgrounds admit at least one extra
Killing spinor in addition to 16 standard Killing spinors, backgrounds can be
reduced to the form with H=A_{mn}(x^-)x^mx^n and \xi(x^-), modulo coordinate
transformations. We examine further the cases in which the extra Killing
spinors are characterized by a set of Cartan matrices. Solving Killing spinor
equations, we find IIB pp-wave backgrounds which admit 18, 20, 24 and 32
Killing spinors.
