Is there a word that means "every four weeks"?

Per Google, bifortnightly and bi-fortnightly together have been used about 5000 times on the web, frequently as objects of ridicule rather than as serious terms for "four-week-ly", occasionally as examples of misunderstanding of whether bi is a multiplier or a divider.

Although the lunar cycle is often thought of as 28 days, lunarly doesn't actually work to indicate 28 days, because the moon's sidereal period is only 27.3 days.

Regarding quadweekly and quadriweekly, I like quatriweekly or quatri-weekly better. Quadroon and quadrant, for example, use quadr- as one-fourth, while quatrain uses quatr- as four; but the roots of all of them are closely related to words meaning four.

Is there a compelling reason you cannot use "every four weeks"? The advantage of using the phrase is that there is less possibility of being misunderstood.

EDIT: You could also word it as "four-week" in the context you give in your comment below.

There's nothing that's actually better than "every four weeks" unless this distinction comes up so much that your office creates their own jargon for it. (See above for the lovely fwaply.)

The problem with trying to sound clever by coining something from roots and prefixes is that the people who grok quadriweekly or quadweekly quickly and intuitively will also understand it's kinda off, since week is Germanic.

The best you've got is four-weekly unless you're showing off with tetrahebdomadally, quadriseptimanally, or duodetrigintally.