The question how an agent is affected by its embodiment has attracted growing attention in recent years. A new field of artificial intelligence has emerged, which is based on the idea that intelligence cannot be understood without taking into account embodiment. We believe that a formal approach to quantifying the embodiment's effect on the agent's behaviour is beneficial to the fields of artificial life and artificial intelligence. The contribution of an agent's body and environment to its behaviour is also known as morphological computation. Therefore, in this work, we propose a quantification of morphological computation, which is based on an information decomposition of the sensorimotor loop into shared, unique and synergistic information. In numerical simulation based on a formal representation of the sensorimotor loop, we show that the unique information of the body and environment is a good measure for morphological computation. The results are compared to our previously derived quantification of morphological computation.