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The observation of the bright pulses and dark square pulses in a graphene-oxide saturable absorber (GOSA) passively mode-locked ytterbium-doped fiber laser has been investigated experimentally. Bright pulses are achieved at a pump power of ~ 200 mW. However, the dark-square-pulse generation starts at a much higher pump power of ~ 450 mW. At the maximum pump power of 600 mW, the dark-square-pulse bunches and harmonic mode locking (HML) can be also obtained by tuning the polarization controller (PC) to different orientations. It is the first demonstration of the bunches and HML of dark square pulses in a GOSA passively mode-locked ytterbium-doped fiber laser with large normal dispersion cavity.