Recently, substantial attention has been paid to improve the spectral efficiency of communication setups using different spectrum sharing techniques. This paper studies the ergodic achievable rate of spectrum sharing channels in the case where the primary licensed user is equipped with a sequential decoder, while there is no connection between the transmitters. Assuming Rayleigh block-fading channels, the unlicensed user ergodic achievable rate is obtained under an extremely hard constraint where no interference is tolerated by the licensed user receiver. Simulation results show that using sequential decoders there is considerable potential for data transmission of the unlicensed user with no performance degradation of the licensed user. Moreover, in contrast to previously proposed schemes, the network sum rate increases by implementation of sequential decoders.