This paper reports AFM observations of the interface of twinned martensite in a Cu-14wt%Al -3.4wt%Ni alloy with an Ms temperature of 10degreesC and an As of 35degrees. Single isolated plates of martensite were produced in electropolished samples by careful cooling to just below Ms or by applying a compressive stress. These plates were twinned, consisting of lamellae of martensite "parent" (A) and twin (B) volumes. The average width fraction of Twin A was 0.667, close to the theoretical value of 0.698. Side-plates extending beyond the habit plane were observed, being associated with the smaller of the two twin volumes (Twin B). This structural feature was common to both thermal and stress-induced martensite plates. The twin plane was close to a variant of the (3 3 1)beta(1) habit plane, and the extension of twin B ahead of the general interface, with its own twinned substructure, is inferred to be related to the plate growth mechanism.