I analyse central bank transparency when the central bank's objective function is its private information. Non-transparency exists when the public does not observe the action of the central bank and an unobservable component of the inflation-control error keeps the public from using its observation of inflation to infer perfectly the central bank's action, and hence, the central bank's objective. The degree of transparency is defined as the fraction of the inflation-control error that is observable. This notion is similar to that of Cukierman and Meltzer [9], Faust and Svensson [15], [16] and others. I find a number of results; some are different than what previous authors have found and others are novel. I demonstrate that non-transparent central banks with private information inflate less than central banks in a regime with perfect information. Moreover, in contrast to transparent central banks with private information, non-transparent banks with private information respond optimally to shocks; lower inflation is not at the expense of flexibility. Increased transparency lowers planned inflation, but surprisingly, it can worsen the public's ability to infer the central bank's objective function. I find that, no matter what their preferences, central banks and societies are made better off by more transparency. I further demonstrate that the transparent regime is not the same as the non-transparent regime when non-transparency goes to zero. I show that planned inflation is not necessarily lower in the transparent regime than in the non-transparent regime. However, numerical results suggest that all central banks and societies are better off in the transparent regime.