The drone - dubbed Aquila -  flew for one hour and 46 minutes in Arizona.
On Aquila's maiden voyage last summer, the autopilot system was confused by heavy wind and crash-landed.
This time, the drone flew at an altitude of 3,000ft, a long way from Facebook's intended 60,000ft goal.
The social network has ambitious plans for its drone fleet and eventually wants to have them communicating with each other via lasers and staying in the air for months at a time.
The test - which took place in May but is only now being made public - went "perfectly", according to a blog post detailing the flight.
Facebook had initially heralded its June 2016 test a success but later admitted the drone had crashed on landing.
The crash was only revealed when it emerged that it had been investigated by the National Transportation Safety Board.
This time, the engineering team added "spoilers" to the wings to increase drag and reduce lift during landing. They also modified the autopilot software and applied a smoother finish to the craft.
The team filmed the landing and included the video in the blog post.
Director of aeronautical platforms Martin Luis Gomez said the drone had suffered "a few minor, easily repairable dings".
Aquila - which has a wingspan of a Boeing 737 - is part of Facebook's ambitious plans to connect the world to the internet.
This week, it announced that it has two billion users, more than a quarter of the world's population.

Rescuers earlier ended efforts to find the body of Jeffrey Bush, 36, whose bedroom was engulfed by the 6m (20ft) hole on as he slept on Thursday night.
Sinkholes are common in parts of Florida, although most are quite small.
Experts are trying to ascertain how far the underground cavity reaches and whether more homes are at risk.
All homes near to the house in Seffner - a suburb of 8,000 people 25km (15 miles) east of central Tampa - have been evacuated.
Officials have created a 100ft-wide safety zone fearing the top of the sinkhole is growing.
The house covers most of the hole, and a local official said crews would try to move the building forward to enable surviving family members to retrieve their belongings from it.
"We don't know, in fact, whether it will collapse or whether it will hold up,'' said Hillsborough County Administrator Mike Merrill.
On Sunday, the demolition crews left standing only a few walls of the house.
They were proceeding as carefully as possible to salvage at least some of the home's contents for five survivors.
A Bible, family photos and a woman's purse were among the items saved.
The demolition is expected to be completed on Monday and experts would then examine the hole.
Just before the crews started their work, 35-year-old Jeremy Bush, who had tried to save his brother, was seen praying outside the house.
Five people escaped unharmed, after hearing a loud crash and Jeffrey Bush screaming as the earth crumbled below the house.
Jeremy Bush said he jumped into the chasm to dig his brother out but failed. He was later rescued by police.
Rescuers then used listening devices and cameras at the scene, but found no signs of life.
"There's no way of possible survival," said fire rescue spokeswoman Jessica Damico on Saturday.
Mr Bush told reporters that someone had visited the four-bedroom house some weeks ago to check for sinkholes and other issues but found nothing wrong.
"And a couple of months later, my brother dies. In a sinkhole," he said.
Florida state law requires home insurers to provide coverage against sinkholes.
Experts say much of Florida sits on a system of limestone caverns which are subject to water erosion, causing them to collapse.

The 20-year-old France international was fined and suspended until Monday for missing Thursday's training, but the ban has been extended indefinitely.
Dortmund met with Barcelona's representatives but the Spanish club did not meet their valuation.
The German club say that Dembele moving to Barca is "not currently likely".
Dortmund director of football Michael Zorc said: "Our focus now is on preparation for the Bundesliga opening match in Wolfsburg [on 19 August]. Dembele, of course, has the opportunity to complete an individual training session outside the group."
Dortmund signed Dembele on a five-year deal from Rennes in May 2016.
Facebook has completed a second test of a solar-powered drone designed to bring internet access to remote parts of the world.
[NEXT_CONCEPT]
Demolition crews have partially razed the home of a man presumed dead after he was swallowed up by a sinkhole in Florida.
[NEXT_CONCEPT]
Borussia Dortmund have suspended forward Ousmane Dembele "until further notice", three days after the club rejected a bid from Barcelona.