We describe the design, construction, and operation of a new type of microwave spectrograph which allows the measurement of the resonant transitions of transient or otherwise short‐lived species. The spectrograph is composed of three parts: a Fabry–Perot cavity, a pulsed supersonic nozzle as a source for the sample, and the pulsed microwave Fourier transform method. Following a detailed discussion of the three above components in the spectrograph, the operation of the entire system is described and several examples are given.