In executing a voluntary movement, one is faced with the problem of translating a specification of the movement in task space (e.g. a visual goal) into a muscle recruitment pattern. Among many brain regions, the primary motor cortex (MI) plays a prominent role in the specification of movements. In what coordinate frame MI represents movement has been a topic of considerable debate. In a two-dimensional wrist step tracking experiment, Kakei et al. 1999 described some MI cells as encoding movement in a muscle coordinate frame and other cells as encoding movement in an extrinsic coordinate frame. This result was interpreted as evidence for a serial cascade of transformations within MI from an extrinsic representation of movement to a muscle-like representation. However, we present a model that demonstrates that, given a realistic extrinsic-like representation of movement, a simple linear network is capable of representing the transformation from an extrinsic-space to the muscle recruitment patterns implementing the movements on which Kakei et al. 1999 focused. This suggests that cells exhibiting extrinsic-like qualities can be involved in the direct recruitment of spinal motor neurons. These results call into question models that presume a serial cascade of transformations terminating with MI pyramidal tract neurons that vary their activation exclusively with muscle activity. Further analysis of the model shows that the correlation between the activity of an MI neuron and a muscle does not predict the strength of the connection between the MI neuron and muscle. This result cautions against the use of correlation methods as a measure of cellular connectivity.