We study the propagation properties (intensity, degree of coherence and scintillation) of a new class of beams in a turbulent atmosphere, which are called Hermite non-uniformly correlated (HNUC) beams. The results show that the beams not only have lower scintillation but also higher intensity than Gaussian-Schell model (GSM) beams over certain propagation ranges. We can adjust the beam order of HNUC beams to enhance the intensity of the beam in the receiver plane and, simultaneously, reduce the detrimental scintillation, and we can also adjust the coherence length of HNUC beams to optimize the effects of a given propagation distance between a signal transmitter and a receiver. (C) 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement