The aim of the paper is to verify whether the USD/EUR exchange rate market is efficient. The fundamental parity condition for testing foreign exchange market efficiency is represented by the uncovered interest-rate parity (UIP). Therefore, the UIP hypothesis verification accounts for the crucial part of the paper. The efficiency of the USD/EUR market is tested by applying the conventional UIP regression approach and orthogonality test of the forward rate forecast error. The results show that it is hard to say definitely that USD/EUR foreign exchange market is inefficient. The slope coefficient in UIP regression occurs to be negative, which implies the failure of uncovered interest-rate parity. However, there are no foundations to reject the UIP hypotheses in the time of financial crisis of 21st century. Moreover, the article presents that the forward forecast error is not orthogonal to both its lagged value and the interest rate differential. Thus, the semi-strong foreign exchange market efficiency hypothesis is rejected for the USD/EUR market.