Will I be charged to replace a a faulty replacement?

I didn't know how to word this question but I replaced my iPhone 4 which had a fault and because it was out of warranty I paid to get a replacement which is fair enough. But only a month after using it I have discovered that the replaced phone is faulty (the LED light will not turn off). I am planning on taking it back to the Apple Store but I am afraid that I will have to pay for a new one since the phone is out of warranty. So will I be charged for a new one? If so, why should I have to pay for a replacement if Apple gave me a faulty replacement in the first place?