A brain-computer interface (BCI) can be used to control a limb neuroprosthesis with motor imaginations (MI) to restore limb functionality of paralyzed persons. However, existing BCIs lack a natural control and need a considerable amount of training time or use invasively recorded biosignals. We show that it is possible to decode velocities and positions of executed arm movements from electroencephalography signals using a new paradigm without external targets. This is a step towards a non-invasive BCI which uses natural MI. Furthermore, training time will be reduced, because it is not necessary to learn new mental strategies.