  In the paper "Direct Images, Fields of Hilbert Spaces, and Geometric
Quantization", Lempert and Sz\H{o}ke proved that any flat analytic Hilbert
field will induce a hermitian Hilbert bundle and gave an example of a flat
Hilbert field that does not induce any Hilbert bundle. In this paper, we will
provide an example of an analytic Hilbert field that does not induce any
Hilbert bundle.
