Reduced order Disturbance OBservers (DOB) have been proposed in Kim et al. (2010) and Kim and Rew (2013) for continuous-time and discrete-time linear systems, respectively. The existence condition of the promising algorithm has been established but is not straightforward to check. This work further improves the reduced order DOB design by formulating it as a functional observer design problem. By carefully designing the state functional matrix, a generic DOB is resulted with an easily-checked necessary and sufficient existence condition and an easily-adjusted convergence rate. It is also shown that both the reduced order DOB in Kim and Rew (2013) and the full order DOB in Chang (2006) are special cases of this new DOB. (C) 2018 Elsevier Ltd. All rights reserved.