Upon motion initiated by any member and adopted by the unanimous vote of the members present (but not less than a majority of all the members), the Board of Appeals shall review, at a rehearing held upon notice given as upon an original hearing, any order, decision or determination of the Board not previously reviewed. Upon such rehearing and provided that it shall then appear that the rights vested prior thereto in persons acting in good faith in reliance upon the order, decision or determination reviewed will not be prejudiced thereby, the Board may, upon the concurring vote of all members then present, reverse, modify or annul its original order, decision or determination.