A 3D CAPTCHA using mental rotation, called YUNiTi CAPTCHA, has been proposed as an advanced system to enable discrimination between computers and humans. YUNiTi CAPTCHA is performed in a “cognometric” mental rotation task. We point out that YUNiTi CAPTCHA has a vulnerability to some pattern matching attacks, which choose the most similar images to a question image among a list of candidate images. We propose a new mental rotation CAPTCHA, called Directcha, to cope with the attacks. Directcha requires users to perform a “spatiometric” mental rotation task, in which users answer the direction of one 3D object in a question image. Directcha uses only one 3D object in the question image, so malware cannot break Directcha using pattern matching attacks. We implemented a prototype of Directcha and carried out basic experiments to test its usability. The results showed that, even though Directcha has higher attack tolerance than YUNiTi CAPTCHA, Directcha has nearly the same level of usability (correct response rate and response time) as that of YUNiTi CAPTCHA. We also describe threats to the security of Directcha.