In this paper, a new transmit alternate laser selection (TALS) scheme for FSO communication systems using intensity modulation and direct detection (IM/DD) over atmospheric turbulence and misalignment fading channels is presented when limited time diversity is available in the turbulent channel. Assuming channel state information (CSI) at the transmitter and receiver and a time diversity order (TDO) limited, we propose the transmit diversity technique based on the rotating selection of TDO out of the available L lasers corresponding to the optical paths with greater values of scintillation. Implementing repetition coding with blocks of TDO information bits, each information bit will be retransmitted TDO times using the TDO largest order statistics in an alternating way. Closed-form asymptotic bit error-rate (BER) expressions are derived when the irradiance of the transmitted optical beam is susceptible to moderate-to-strong turbulence conditions, following a gamma-gamma (GG) distribution, and pointing error effects, following a misalignment fading model where the effect of beam width, detector size and jitter variance is considered. Fully exploiting the potential time-diversity TDO available in the turbulent channel, a significant diversity gain is achieved, providing a diversity order of (2L + 1 − TDO)TDO/2.