A new asynchronous pipeline is presented for the self-timed design discipline of quasi-delay insensitivity with dual-rail encoding and four-phase handshaking. The function blocks of the pipeline consist of a universal gate (presented in the appendix) which is particularly simple, comprising only the conventional nand and nor gates, and is supported by an equally simple development method. The simple quadgate enables optimisation techniques for completion- detection circuitry and pipeline architecture. The pipeline is reported to compare favourably with analogous designs and is demonstrated here on a selection of 32-bit adders, simulated on 10,000 pairs of random inputs.