Yes and no! There are three Full Moons between June 1 and July 31. The second of these falls within a few hours of midnight on June 31. This means that in North America, we will have two FUll Moons in June and one in July, but in Great Britain and Europe, they will have only one Full Moon in June, but two in July! My previous answer was based on Universal Time reckoning which is appropriate to British and European observers. Observers in the United States are 5-8 hours earlier which is just enough time to shift the second Full Moon from July 1 to June 31. Have a look at the June 1996 Astronomy or Sky and Telescope magazines for more on this amusing situation!