Studies of inflation targeting make the distinction between strict and flexible inflation targeting. The problem of strict inflation targeting has so far been analysed by treating it as a special case of a standard optimal control problem and the algorithms used have not provided an exact solution. This paper presents a formal solution to the problem of strict inflation targeting in a economy with a forward-looking variable. It explains how the results can be applied with more than one forward-looking variable. It also draws on relevant control theory results.