Summary: This paper considers the design of binary bandlimited signals for transmission over a channel with additive white Gaussian noise, the signals to be received by a memoryless correlation detector. A signal waveform is found which allows communication at the Nyquist rate without intersymbol interference and with 1.3 db degradation compared to an optimum communication system. Other waveforms, consisting of the sum of a few prolate spheroidal functions, are also investigated.