The phrase "a second round of negotiations" is correct and usable in written English.
It can be used when referring to a subsequent series of discussions or talks aimed at reaching an agreement or resolving a dispute.
Example: "After the initial discussions, both parties agreed to enter a second round of negotiations to finalize the terms of the contract."
Alternatives: "a follow-up negotiation" or "a subsequent negotiation round".
After a second round of negotiations in the United States in mid-January, the talks again broke off.
Subsequently, there was a second round of negotiations on the stations, and Viacom walked away again, thinking the price was too high.
The US and Cuba have held a second round of negotiations on restoring diplomatic relations after a half-century interruption, although an immediate breakthrough appeared unlikely.
On April 30, the World Health Organization will start a second round of negotiations on terms of a global treaty to control tobacco.
The possibility of moving all or most of the division is to be discussed when Mr. Lawless returns here next month for a second round of negotiations.
Last Wednesday, Mr. Bush's top advisers met by video teleconference for another inconclusive discussion on whether to enter a second round of negotiations with North Korea and how to handle the back-to-back visits.
Maybe that terrible deal, in which Republicans ended up getting more than their opening bid, was the best he could achieve — although it looks from here as if the president's idea of how to bargain is to start by negotiating with himself, making pre-emptive concessions, then pursue a second round of negotiation with the G.O.P., leading to further concessions.
As the Press Association reports, after a third round of negotiations with the Scottish National party yesterday, Moore said there was "goodwill on both sides" over the issue.
A8 Talks on World Tobacco Pact During a third round of negotiations in Geneva, the World Health Organization and other groups wrangled over a proposed global ban on promoting cigarettes and provisions covering the industry's liability.
