A stability analysis for the cyclotron-maser instability in the presence of a nongyrotropic electron distribution is presented. The model configuration describes a uniformly magnetized cold ambient plasma that contains a relatively diffuse suprathermal electron component coherently bunched in gyrophase. The stability of perturbations propagating parallel to the ambient magnetic field is considered, and substantial growth rates are found to occur. The results are contrasted with those found for a comparable gyrotropic loss-cone distribution, and it is found that the nongyrotropic instability is characterized by substantially higher growth rates.