Summary. A set of recurrence relations similar to that of Kennett suitable for SH-wave generation in an (n+ l)-layered half-space is presented. The recurrence relations contain no growing terms, thus providing a stable and efficient algorithm for computing complete SH synthetic seismograms. The complete expansion of these recurrence relations gives the explicit form of the transfer function for SH-waves. The transfer function for a point source in layer s of the stratification is a series of 2n terms in the denominator and a series of 2n−s+1 terms in the numerator. The result of Wang from ray summation is shown to be a special case of our general result. Numerical comparison of the algorithm of this paper with the propagator matrix method is also made.