The dynamics of helical decaying homogeneous turbulence is investigated in direct numerical simulations at moderate Reynolds numbers. A new initialization procedure is presented that allows one to control both the energy and the helicity spectral density of the initial flow field. It is observed that large initial helicity impedes the transfer of energy toward smaller scales, inhibits the buildup of enstrophy, and reduces dissipation for several turnover times. Also, the skewness and flatness of the velocity derivatives reach values typical of turbulence much later than in comparable flows without helicity. However, these effects are significant only if the helicity of the flow is quite high. In simulations with small or vanishing initial helicity it is found that the fluctuations of the average helicity and the helicity spectral density lie within the range suggested by a quasi-Gaussian approximation. This suggests that at moderate Reynolds number spontaneous fluctuations of helicity are not large enough to directly influence the energy transfer.