"Kinetic arrest (KA) of martensitic transformation (MT) has been observed in as-solidified Ni52.2Mn34.3In13.5 melt-spun ribbons; a characterization by dc magnetization measurements was carried out. These alloy ribbons transform martensitically from a single austenitic (AST) parent phase with B2-type crystal structure. For an applied magnetic field U0H of 1 T and up to 9 T, a moderate but progressive KA of the MT is observed. The metastability of the non-equilibrium field-cooled glassy state was characterized by introducing thermal and magnetic field fluctuations. It was found that the total magnetization difference (??) between the zero field-cooling (ZFC) and field-cooling (FC) pathways of the temperature dependence of magnetization ??(T) shows irreversible and reversible components; the former decreases as the temperature decreases. After a short thermal annealing of 10 min at 1073 K AST shows a highly ordered L21-type crystal structure and the kinetic arrest of martensitic transformation is no longer observed suggesting a connection between the crystal structure order of austenite and the appearance of the kinetic arrest phenomenon."