In this work, a novel Dynamic Movement Primitive (DMP) formulation is proposed which supports reversibility, i.e. backwards reproduction of a learned trajectory. Apart from sharing all favourable properties of the original DMP, decoupling the teaching of position and velocity profiles and bidirectional drivability along the encoded path are also supported. Original DMP have been extensively used for encoding and reproducing a desired motion pattern in several robotic applications. However, they lack reversibility, which is a useful and expedient property that can be leveraged in many scenarios. The proposed formulation is analyzed theoretically and its practical usefulness is showcased in an assembly by insertion experimental scenario.