In random number generation (RNG) tasks, used to assess executive functioning, participants are asked to generate a random sequence of digits at a paced rate, either verbally or by writing. Some previous studies used an alternative format in which participants had to randomly press different response keys, assuming that this task version demands the same cognitive processes as those implied in the standard version. The present study examined the validity of this assumption. To this end, the construct validity, reliability, and sensitivity of a conceptually similar task version of the key-press task were examined. Participants had to randomly click on, or point to, the digits 1-9, laid out orderly in a 3 × 3 grid on a computer screen. Psychometric properties of this task were examined, based on the performance of 131 healthy participants and 80 patients with cognitive decline. The results suggest that the click/point RNG task version can be used as a reliable and valid substitute for standard task versions that use the same response set and response pacing rate as those used in the present study. This task might be a useful alternative, demanding no separate recording and recoding of responses, and being suitable for use with patients with speech or writing problems.