The Transport Salaried Staffs' Association will walk out with Aslef, RMT and Unite on 5 August in a row over servicing the new Night Tube service.
London Underground said it had made a "fair" offer and would continue to be available for talks.
The four unions previously walked out on 9 July causing the entire Tube network to shut down.
Talks had been held at conciliatory service Acas on Tuesday.
But TSSA's general secretary Manuel Cortes said: "We were expecting to agree a framework to discuss all our concerns over staffing levels and safety at the Night Tube as well as the pay issues.
"But all we got was a repeat of the 'take or leave' final pay offer which has already been rejected and no detailed talks on the Night Tube. We are willing to negotiate, they clearly are not."
Steve Griffiths, London Underground's Chief Operating Officer, said: "We have made a very fair and reasonable offer on pay and the introduction of the Night Tube and we continue to urge the trade unions to put it to their members.
"We will be at ACAS this week for further discussions to resolve this issue and trust the trade unions will be too."
The row is over a 2% average pay rise offer for LU members and workers' terms and conditions linked to plans to introduce an all-night Tube service on the Jubilee and Victoria lines and and most of the Central, Northern and Piccadilly lines.
Last week's strike saw long delays and rush hour began earlier than normal as commuters tried to find alternative ways to get to and from work.

The world number one responded to a post on Instagram that described the American as "very average".
Spieth replied: "Couldn't be further from the truth troll. Go do research before hating."
Defending champion Spieth bogeyed five of his first seven holes to trail the leaders by seven strokes on two over.
The 22-year-old shot 30 under par to win the Hyundai Tournament of Champions in January but his form has slumped recently, with a missed cut in the Northern Trust Open followed by a 17th-place finish in last week's WGC-Cadillac Championship.
World number two Rory McIlroy backed his rival, posting on Twitter: "No, he's not TW (Tiger Woods), he's not slumping and he's not done. He's a double major winning 22 year old. He'll be just fine!!"
Spieth, 22, also took exception to a post on the PGA Tour's official Twitter account that he thought used one of his remarks out of context.
It highlighted a joke from the his post-round interview when asked whether he could accept having an occasional off day.
The PGA post, later deleted, read: "What good is kicking the door other than hurting my foot and [having to] withdraw?"
Spieth responded: "Seriously? That's the quote you're going to use out of that article?"
He later explained: "I was a little upset. It made it seem like I was OK with getting hurt and withdrawing. I was frustrated with that."
There were signs of encouragement for the Masters and US Open champion after his dreadful start as he recovered for a second round of 68, two shots inside the cut.
"Today was all about the cut," he said.
"I actually did pretty well to make six [at the first hole]. I thought it was really strong what we did after that. For the first 20 holes to be at six over and we finished at two over, [there are] only positives going forward."
Steve Stricker holed a 150-yard shot for an eagle two in a 66 as he moved into the joint lead on five under with fellow American Will Mackenzie (67).
They lead compatriots Daniel Berger (68) and Bill Haas (67), and Canada's Graeme DeLaet (66), by one stroke.
England's Danny Willett is level par after a one-over 72, while Ian Poulter is one over after a level-par 71 and Scotland's Russell Knox improved to to two over with a 69.
Luke Donald joined Knox after also firing a two-under 69.
However, Northern Ireland's Graeme McDowell (72) and Martin Laird (75) were among those who missed the cut.
A fourth union has announced it will be take part in a 24-hour Tube strike next month in a row over pay and conditions.
[NEXT_CONCEPT]
Jordan Spieth defended himself after being called "garbage" by an internet "troll" as he narrowly made the cut at the Valspar Championship in Florida.