PRAGUE (Reuters) - The presidents of the Czech Republic and Slovakia on Wednesday embarked on a new era of cordiality more than six years after Czechoslovakia‘s peaceful but prickly "Velvet Divorce". Slovak President Rudolf Schuster, in Prague on his first trip abroad since being sworn in June, and his Czech host, Vaclav Havel, pledged frequent visits to improve ties which had glazed over in the frosty post-split period. "The possibilities we have are not being fully used. We‘ve known each other a long time, there are no language barriers, companies know each other," Schuster said at a joint news conference. Havel warmly welcomed the result of Slovakia‘s first direct presidential election where Schuster defeated former nationalist Prime Minister Vladimir Meciar to fill the post which had been vacant for more than a year because of political infighting. Meciar was frequently antagonistic toward Prague and especially Havel after the split in 1993. Havel said Schuster‘s quick visit to Prague after his inauguration represented a "clear signal" of the intentions to mend relations between the former federation partners. Both leaders said they would meet frequently on issues ranging from Slovakia‘s application for NATO membership — which the new NATO members, the Czechs, strongly support — to trade and migration problems in the region and throughout Europe. Czech and Slovak officials have met on only a handful occasions since the split which came in response to long-standing demands from nationalists in Bratislava. The "no-fault" divorce meant property was to be split in a two-to-one ratio, favouring the Czechs to reflect the population of the former 15 million-strong Czechoslovakia. Both presidents, more ceremonial figureheads than chief executives in their political systems, said on Wednesday that they would throw their support behind their governments‘ attempts to resolve remaining property issues this year. The most delicate is the settlement of assets of the former Communist-era state bank, with four tonnes of gold claimed by Bratislava still being held in Prague. Schuster said he could see the adoption of a so-called "zero option", currently under discussion, where both sides would simply excuse all claims against the other. "No side should come away with the feeling that they won or lost," Schuster said. Havel added that a joint declaration resolving the property issue may be ready by November.