While Yugoslavia is being consumed in the flames of a murderous civil war, another small Balkan state will go out of existence on New Year's Day with little fanfare or commotion, and two new countries will be born. Unlike the Yugoslavian conflagration, this is a friendly divorce. The vanishing nation is Czechoslovakia. Its ethnic parts are being re-created as the independent Czech Republic and Slovakia.

The lack of acrimony or conflict, however, does not mean that the division is wise or will be easy. Most observers believe Czechoslovakia would have been better off if it had stayed as a single entity.The Czech Republic, with 10 million inhabitants and much of Czechoslovakia's industrial strength, will be the economically strongest of the two states. Slovakia's 5 million citizens will face tougher times, more unemployment and higher inflation. Private Slovakians and even Slovakian companies are putting their funds into Czech banks. New taxes will raise the cost of living about 7 percent overnight in both nations when the breakup occurs.

But Slovakians have been among those who pushed the hardest for the division. Few Czechs wanted the breakup and most feel badly about it. The Slovakians had argued that free-market reforms and other changes in the former communist-run state must go slower and be tailored to local needs.

However, Czech leaders must shoulder a share of the blame because of their take-it or leave-it attitudes over political issues and their failure to push for a referendum that might have kept the country together.

Dividing up an entire nation has proved to be a difficult task. For example, the military has shipped some 2,000 railroad trains filled with supplies and equipment between the two states. Officials had to figure out how to divide up everything from jet planes to two tons of paint. The job was complicated by the fact that most defense installations were in Czech territory. At least the bullets were handed over instead of being shot over. Soldiers were given the option of which army they wanted to serve.

Czechoslovakian embassies all over the world are being shut down. Many will not reopen, and government workers are being laid off at home as well. Dividing up government documents was difficult. About 2,800 large and small treaties with foreign nations had to be discontinued or transferred.

Contracts with foreign nations were split 2-1 in favor of the Czech Republic since it is twice as large. The same is true of debts and loans. Some 7.5 tons of gold reserves are still disputed since Slovakia says it owned the gold while it was independent in World War II. Thousands of other, smaller issues are being ironed out.

At this point, the rest of the world can only wish Slovakia and the Czech Republic well and hope each survives and prospers.