Radar clutter is distinguished from thermal noise by being caused by random reflection of transmitted electromagnetic energy. This paper considers what may be done by means of linear filtering to improve the detection of small radar signals in the presence of this clutter. Defining the signal‐to‐clutter ratio as the ratio of the peak signal to the rms value of the clutter, the optimum linear filter is derived for enhancing this ratio. The optimum filter has a frequency characteristic given by the conjugate of the voltage spectrum of the transmitted pulse divided by the power spectrum of the clutter. The synthesis of the optimum filter and various approximations to it are considered. The influence of these filters upon the signal‐to‐thermal‐noise ratio is also investigated. Finally, the influence of the second detector upon the signal‐to‐clutter or signal‐to‐noise ratio is considered.