Based on the measurements of spectra and polarization of low-temperature (5K) microphotoluminescence excited by stabilized continuous-wave laser pumping, we find a new type of isolated emitters formed due to the dislocations in crystalline CdZnTe. For an emitter of this type, zero-phonon luminescence is located 30–50 meV above the usual dislocation luminescence and is subjected to giant fluctuations of spectral position (~10 meV) and intensity. A noticeable degree of linear polarization in the plane containing directions indicates the strongly anisotropic nature of the corresponding electronic states and confirms their connection with dislocations.