My iPhone 4S won't restore.

I updated my iPhone and when it turned back on the screen came up with the picture that tells me to connect it to itunes. The computer that I normally use and has my itunes is broken so i connected it to my sisters. When I connected it, it said that my iphone is in recovery mode and it must be restored and updated before it can be used with iTunes. I restored it and it went through the whole process and then it said that my phone has been restored to factory settings and to leave it connected to itunes but when my phone restarts, the same picture telling me to connect it to itunes shows up and i've restored it multiple times and it does the same thing!