Two well-known disturbance decoupling problems are considered. A checkable necessary and sufficient condition is derived under which the disturbance decoupling problem with static measurement feedback (DDPKM) is solvable for a class of multi-input and multi-output linear time-invariant systems, which have a left invertible transfer matrix function from the control input to the controlled output. The set of all solutions that solve the DDPKM is constructed and parametrized explicitly. This set is then used to solve the disturbance decoupling problem with static measurement feedback and with internal stability (DDPKMS).