  We consider the ground-state properties of the s=1/2 Ising chain in a
transverse field which varies regularly along the chain having a period of
alternation 2. Such a model, similarly to its uniform counterpart, exhibits
quantum phase transitions. However, the number and the position of the quantum
phase transition points depend on the strength of transverse field modulation.
The behaviour in the vicinity of the critical field in most cases remains the
same as for the uniform chain (i.e. belongs to the square-lattice Ising model
universality class). However, a new critical behaviour may also arise. We
report the results for critical exponents obtained partially analytically and
partially numerically for very long chains consisting of a few thousand sites.
