  This paper studies a new set of mixed boundary conditions in Euclidean
quantum gravity. These involve, in particular, Robin boundary conditions on the
perturbed 3-metric and hence lead, by gauge invariance, to Robin conditions on
the whole ghost 1-form. The corresponding trace anomaly is evaluated in the
case of flat Euclidean 4-space bounded by a 3-sphere. In general, this anomaly
differs from the ones resulting from other local or non-local boundary
conditions studied in the recent literature.
