Stepped fine structure of temperature and salinity observed in the Tyrrhenian Sea at a depth of between 600 and 1400 m is an established feature which has been studied over a number of years. At these depths the temperature and the salinity both decrease with depth, so it is temping to relate this fine structure to salt finger convection. Recent observations with an optical device have shwon that the fingers do not exist continuously across the interfaces between the steps but are found only in certain regions inside the interface. This discontinuous finger structure had not been observed previously in the laboratory, and this paper describes some experiments in which the breakup of salt fingers in an interface is documented. The conditions under which the fingers break up are investigated, and some implications of these new observations to the interpretation of oceanic fine structure are discussed.