Objective. Steady-state visually evoked potential (SSVEP)-based brain–computer interfaces (BCIs) allow healthy subjects to communicate. However, their dependence on gaze control prevents their use with severely disabled patients. Gaze-independent SSVEP-BCIs have been designed but have shown a drop in accuracy and have not been tested in brain-injured patients. In the present paper, we propose a novel independent SSVEP-BCI based on covert attention with an improved classification rate. We study the influence of feature extraction algorithms and the number of harmonics. Finally, we test online communication on healthy volunteers and patients with locked-in syndrome (LIS). Approach. Twenty-four healthy subjects and six LIS patients participated in this study. An independent covert two-class SSVEP paradigm was used with a newly developed portable light emitting diode-based 'interlaced squares' stimulation pattern. Main results. Mean offline and online accuracies on healthy subjects were respectively 85 ± 2% and 74 ± 13%, with eight out of twelve subjects succeeding to communicate efficiently with 80 ± 9% accuracy. Two out of six LIS patients reached an offline accuracy above the chance level, illustrating a response to a command. One out of four LIS patients could communicate online. Significance. We have demonstrated the feasibility of online communication with a covert SSVEP paradigm that is truly independent of all neuromuscular functions. The potential clinical use of the presented BCI system as a diagnostic (i.e., detecting command-following) and communication tool for severely brain-injured patients will need to be further explored.