  Let J be a monic Jacobi matrix associated with the Cauchy transform F of a
probability measure. We construct a pair of the lower and upper triangular
block matrices L and U such that J=LU and the matrix J_c=UL is a monic
generalized Jacobi matrix associated with the function F_c(z)=zF(z)+1. It turns
out that the Christoffel transformation J_c of a bounded monic Jacobi matrix J
can be unbounded. This phenomenon is shown to be related to the effect of
accumulating at infinity of the poles of the Pad\'e approximants of the
function F_c although F_c is holomorphic at infinity. The case of the
UL-factorization of J is considered as well.
