02/27/2013 at 03:15 PM EST
Better late than never!
More than seven years after saying, "I do"
in a private, low-key ceremony at City Hall in Manhattan in 2005, Matt Damon
, 42, and wife Luciana are going all out with a top-secret destination wedding celebration in April, a source confirms to PEOPLE.
The pair has sent out "save the date" cards to close family and friends, but even the guests do not know the mysterious location of the event.
"They now want to do something bigger," a source tells Page Six
of their planned second wedding.
But "bigger" doesn't necessarily mean the couple's four girls will participate in the ceremony. They are reportedly requesting "no kids" at the destination event.
Reporting by JULIE JORDAN