Yes, HDMI 2.0 can support up to 240 Hz in 1080p resolution. It also supports 144 Hz in 1440p resolution & 60 Hz in 4K resolution. But if you need a more refresh rate in 4K, you will have to use HDMI 2.1 cables that can support up to 120 Hz in 4K & 60 Hz when using 8K resolution.