This is a followup to an earlier question I asked: Does formally etale imply flat? After some remarks I received on MO I noticed that this was answered to the negative by an answer to an earlier question Is there an example of a formally smooth morphism which is not smooth. However, the simple example involves a non-noetherian ring (in fact, a perfect ring; these are seldom noetherian unless they are a field).

So my challenge is to provide an example of a formally etale map of **noetherian** schemes which is not flat, or otherwise proof that for maps of noetherian schemes formally etale implies flat.