HDMI forbids recording as noted at http://en.wikipedia.org/wiki/High-bandwidth_Digital_Content_Protection so you can't record a stream.
To get around this, many use 2 cameras.
Bob
Hello. Here at our school we would like to be able to stream what our video camera is recording (basketball game), to a mounted TV in a different room, via hdmi (or any other way really...whatever is possible). At the same time, we would like to be able to record and save onto a SD card what our camera is viewing, so our coaches will have the copy of their game for coaching use.
Is this possible?

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic