Observations are presented, obtained by in situ straining and conventional TEM, of a transformation mechanism by coordinated secondary twinning predicted by Mullner and King. The material studied is the martensitic phase of a non-modulated Ni-Mn-Ga alloy, which exhibits a microstructure comprising domains of lamellar matrix/twin composites. Straining these specimens induced lamellar domains to transform into their conjugate counterparts. In this process, secondary twinning generates a change of misorientation between the matrix and twin lamellae of the initial domain by nearly 23A degrees. The orientation evolves over a region behind the transformation front about 100 nm in extent.