A theory is given of the highly anomalous kind of second-order martensitic transformation from cubic to tetragonal structure in Mn85Ni9C6 reported in Papers 1 and 2. The phenomena are explained in a natural way, in particular the remarkable fact that on passing through the martensite-start temperature TMS in this type of transformation the unit cell a dimension alters continuously while the c dimension jumps discontinuously. The analysis is based on the elastic free energy of a simplified model of the true crystalline microstructure incorporating just the basic idea of there being alternate layers of the two phases, joined at 001 habit planes without disruption of the lattice. A "critical" power-law relationship connecting the volume ratio of the two phases to the unit cell dimensions is injected using an empirical formula as Ansatz. It is shown that the specimen of Papers 1 and 2 is stressed, below T-MS, by locked-in pressures that rise to about 6 kbar as the transformation proceeds. However, an exercise in fitting the theory to the data of Paper 2 makes it clear that quantitative detail will not be explained until a fuller theory of the elasticity is developed, expanding the free energy well beyond the fourth powers of the elastic distortion parameters and taking proper account of the highly temperature-dependent magnetoelasticity.