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A new partial transmit sequence (PTS) scheme with low computational complexity is proposed, where two search steps are taken to find a subset of phase rotating vectors showing good peak-to-average power ratio (PAPR) reduction performance. In the first step, sequences with low correlation are used as phase rotating vectors for PTS scheme, which are called the initial phase vectors. In the second step, local search is performed based on the initial phase vectors to find additional phase rotating vectors which show good PAPR reduction performance. Numerical analysis shows that the proposed PTS scheme achieves better PAPR reduction performance with significantly reduced computational complexity than the existing low-complexity PTS schemes.