In bitcoin, each transaction's signature is signed with previous owner's private key. Then, how sign the first transaction's signature?
See Bitcoin Wiki. Above image illustrates a byte-map of transaction with each type of TxIn and TxOut.
We should attention at "Coinbase/Generation" (Coinbase means the first transaction in a block). Codebase's script is a arbitary data. Yep, it is random.
Therefore the signature of first transaction of a block is not used.