Computer simulations in which selection acts on a quantitative character show that the randomness of mutations can contribute significantly to evolutionary divergence between populations. In different populations, different advantageous mutations occur, and are selected to fixation, so that the populations diverge even when they are initially identical, and are subject to identical selection. This stochastic process is distinct from random genetic drift. In some circumstances (large populations or strong selection, or both) mutational order can be greatly more important than random drift in bringing about divergence. It can generate a `disconnection' between evolution at the phenotypic and genotypic levels, and can give rise to a rough `molecular clock', albeit episodic, that is driven by selection. In the absence of selection, mutational order has little or no effect.