SanDisk Extreme® Pro™ SDHC™ UHS-1 Card

yes win 7 natively supports exFAT. the camera may be stopping the recording at 4GB file size. it is definitely not a limit of exFAT. I would contact the camera manufacturer and check to see if it is a limitation of the camera firmware. 

  • Scalability to large disk sizes: 64 ZiB[12] theoretical max, 512 TiB recommended max, raised from the 2 TiB limit of FAT32 partitions. Note that the built-in Windows 2000/XP/Vista/7 format utility limits new FAT32 partitions to 32 GiB.[1]
  • Cluster size up to 32 MiB[1]
  • Subdirectory size up to 256 MiB[1]
  • File size limit of 16 EiB[13] (Limited by volume size), raised from close to 4 GiB in FAT32[1]
  • Free space allocation and delete performance improved due to introduction of a free space bitmap
  • Support for up to 2,796,202 files per subdirectory,[2][14] increased from 65,536
  • Support for access control lists (not supported in Windows Vista SP1)[15]
  • Support for TFAT, a transactional file system standard (optionally WinCE activated function)
  • Provision for OEM-definable parameters to customize the file system for specific device characteristics
  • Support for UTC timestamps (starting with Vista SP2)[16]
  • Timestamp granularity of 10 ms (better than previous FAT versions’ 2 s, but worse than NTFS’s 100 ns)[2]