Direct observation of the self-accommodation morphology for orthorhombic martensite in Ti51.0Ni44.4Cu4.6 thin films has been accomplished by transmission microscopy of fine grained (<2μm) material prepared by triode magnetron sputtering. The films were observed to undergo, on cooling, two separate thermoelastic transformations in which the B2 austenite phase first transformed to an orthorhombic martensite with a =.291 nm, b =.425 nm and c =.450 nm followed by transformation to the monoclinic phase at lower temperature. The R-phase transformation was suppressed. Single grains contained as many as eight crystallographic variants of the orthorhombic phase, the majority of which were shaped as parallelograms bounded by {111}Ortho twin planes. The local self-accommodation mechanism produced combinations in which three adjacent variants shared a common {111}B2 pole. Although the majority of B19 variant domains accommodated themselves through {111}Ortho type twinning, a second accommodation mechanism, involving two sets of band-like martensite variants, bounded by {011}ortho twin planes, was also observed. Simultaneous occurrence of the {111}ortho and {011}ortho twinning modes, wihtin a single austenite grain, was not observed.