"strengthening cooperation" is correct and usable in written English.
You can use it when referring to ways in which two or more people, organizations, or countries are working together to achieve a common goal. For example, "The two governments are committed to strengthening cooperation in order to develop new regulations for their shared border."
Member states are seizing dubious objects at their borders, strengthening cooperation among services.
Writing on Facebook ahead of the trip, Mr Modi said the aim is "strengthening cooperation with a traditional friend".
Leaders are expected to agree on a "nine-pillar" plan tomorrow that is intended to become a guide to strengthening cooperation between developed and emerging economies.
The drills, which involve about 100 soldiers from each side, are intended at strengthening cooperation on anti-terrorism, according to China Daily.
One reasonable response would be to seek condemnation by the United Nations Security Council, while expanding military defenses against the North and strengthening cooperation with Japan.
The Slovenian agency focuses on improving the research base in companies and strengthening cooperation between company labs and public research institutions.
We are ready to strengthen cooperation with the US side on this issue".
The real challenge for Europe is not devising institutions or policies to strengthen cooperation between national states.
Despite a rocky start in summer, talks between the IAEA and Iran culminated on November 11 with a Joint Statement on a Framework for Cooperation to strengthen cooperation and communication.
Majdoub is in London to meet transport ministers, Foreign Office officials and the home secretary, Amber Rudd, and to strengthen cooperation with the UK security services.
Most significantly, Italy is leading an effort to repair relations with Russia after the Ukraine confrontation and to strengthen cooperation over Syria.
