Now with warmer weather and more boat traffic, concern is that the barge could hit a boat.
It was last July when a boat slammed into a barge just south of the bridge, killing two people.
There are a number of the construction barges out on the river. But now added pressure is being placed on the contractors to ensure the barges don't break away again.
The Tappan Zee Constructors said in a statement Sunday that one of its barges came loose from its mooring and was recovered an hour later.
The latest runaway barge to head down river from the site of the new bridge was captured in a video as it passed the Half Moon restaurant in Dobbs Ferry late Sunday afternoon.
"This is an unacceptable occurrence and it isn't the first time it has happened," said special advisor to the governor, Brian Conybeare.
They are now putting monetary pressure on Tappan Zee Contractors until they have a corrective action plan in place.
"The Thruway Authority is going to withhold up to $1 million a month in project progress payments to them," said Conybeare.
Mark Rohr, a construction company owner who knows the river, is not surprised the barges have broken free.
"I don't think there is very much they can do but hope their anchors hold," said Rohr. "There is a lot of silt in the bottom of the river. Things don't always get a good grip at the bottom of the river, and that's probably the problem."
And at the Tappan Zee Marina, where Mike Setteducati is getting ready for the upcoming boating season, the concern naturally is for the safety of the pleasure boater.
"They've had a couple break free. We kind of keep our fingers crossed and hope for the best with all of that," said Setteducati.
The river is now crowded with a flotilla of construction equipment as the work on the new replacement bridge continues.
Out on the river, a Coast Guard buoy tender could be seen moving through the construction barges that now dot the sides of the river's main channel.
The construction company has made a request to the Coast Guard to create a zone around the barges prohibiting pleasure boaters from going near the moorings.
The company told the Journal News that it checks mooring tie-offs at least four times during each shift. It says the loose barge was inspected about 45 minutes earlier.
Conybeare says the Thruway Authority is reviewing the company's safety protocols and barge mooring methods. He says TZC has been instructed to install GPS tracking on its barges and other vessels.