An unusually high damping peak has been detected in martensite/martensite double layer Ni-Ti shape memory films. The double layer consisted of two 1-mum thick layers deposited successively at 250 and 385 degreesC from the same target onto a 100-mum Si cantilever substrate. Around room temperature, the individual layers consisted of rhombohedral and monoclinic martensite, respectively. The maximum damping of the martensite/martensite/Si cantilever, occurring at 50 degreesC, equaled Q(-1) = 1.4 x 10(-4) which corresponds to a damping of the martensite/martensite composite of 11%. It is proposed that this extraordinary damping is caused by the interactive formation of B19' and R martensites in the stress coupled layers.