In this paper we consider a two-country New Open Economy Macroeconomics model, and analyze the optimal monetary policy when countries cooperate in the face of a "global liquidity trap"--i.e., a situation where the two countries are simultaneously caught in liquidity traps. The notable features of the optimal policy in the face of a global liquidity trap are history dependence and international dependence. The optimality of history dependent policy is confirmed as in local liquidity trap. A new feature of monetary policy in global liquidity trap is whether or not a country's nominal interest rate is hitting the zero bound affects the target inflation rate of the other country. The direction of the effect depends on whether goods produced in the two countries are Edgeworth complements or substitutes. We also compare several classes of simple interest-rate rules. Our finding is that targeting the price level yields higher welfare than targeting the inflation rate, and that it is desirable to let the policy rate of each country respond not only to its own price level and output gap, but also to those in the other country.