Brain-computer interface (BCI) opens a new communication channel for individuals with severe motor disorders. In P300-based BCIs, gazing the target event plays an important role in the BCI performance. Individuals who have their eye movements affected may lose the ability to gaze targets that are in the visual periphery. This paper presents a novel P300-based paradigm called gaze independent block speller (GIBS), and compares its performance with that of the standard row-column (RC) speller. GIBS paradigm requires extra selections of blocks of letters. The online experiments made with able-bodied participants show that the users can effectively control GIBS without moving the eyes (covert attention), while this task is not possible with RC speller. Furthermore, with overt attention, the results show that the improved classification accuracy of GIBS over RC speller compensates the extra selections, thereby achieving similar practical bit rates.