On a construction of critical graphs which are not sensitive

Let ?(G) be theclosed-set lattice of a graphG. G issensitive if the following implication is always true for any graphG′: ?(G)??(G′)?(G)?G′G iscritical if ?(G)??(G-e) for anye inE(G) and ?(G)??(G+e) for anye in (left( {bar G} right)) where (bar G) is the complement ofG. Every sensitive graph is, a fortiori, critical. Is every critical graph sensitive? A negative answer to this question is given in this note.