In recent years, the readiness potential (RP), a type of pre-movement neural activity, has been investigated for asynchronous electroencephalogram (EEG)-based brain-computer interfaces (BCIs). Since the RP is attenuated for involuntary movements, a BCI driven by RP alone could facilitate intentional control amid a plethora of unintentional movements. Previous studies have mainly attempted binary single-trial classification of RP. An RP-based BCI with three or more states would expand the options for functional control. Here, we propose a ternary BCI based on single-trial RPs. This BCI classifies amongst an idle state, a left hand and a right hand self-initiated fine movement. A pipeline of spatio-temporal filtering with per participant parameter optimization was used for feature extraction. The ternary classification was decomposed into binary classifications using a decision-directed acyclic graph (DDAG). For each class pair in the DDAG structure, an ordered diversified classifier system (ODCS-DDAG) was used to select the best among various classification algorithms or to combine the results of different classification algorithms. Using EEG data from 14 participants performing self-initiated left or right key presses, punctuated with rest periods, we compared the performance of ODCS-DDAG to a ternary classifier and four popular multiclass decomposition methods using only a single classification algorithm. ODCS-DDAG had the highest performance (0.769 Cohen's Kappa score) and was significantly better than the ternary classifier and two of the four multiclass decomposition methods. Our work supports further study of RP-based BCI for intuitive asynchronous environmental control or augmentative communication.