## 1 Introduction
Alignment in the large-scale has also been studied many times, starting with the work of [PERSON] [23], [PERSON]'s research group analyzed the polarization vectors of quasars. Based on a new sample of 355 quasars with significant optical polarization, they found that the polarization vectors of the quasars are not randomly oriented on the celestial sphere [24]. The polarization vectors show an order on a scale of about 1 Gpc. In addition, the average polarization angle rotates with redshift, by about \(30^{\circ}\) per Gpc. Anisotropy in cosmology was later confirmed by many authors--see, for the most recent review, [25]. Two main methods of studying the orientation of galaxies have crystallized over the years. The authors of the first of them are [PERSON] and [PERSON] [26], who in their approach used the statistical analysis of the distributions of galaxy position angles in order to detect possible deviations from the isotropic distribution. As part of the approach, the \(\chi^{2}\), First Autocorrelation and Fourier tests were introduced, which have become a standard method in this type of research [21; 22; 27]. This approach has a flaw, however, in that position angles only give good information about the orientations of galaxy planes for side-viewed galaxies. An alternative method was originally proposed by [PERSON] [28], applied by [PERSON] and [PERSON] [29; 30], and significantly modified by [PERSON] and [PERSON] [9; 31]. It uses not only the position angles of galaxies, but also their ellipticities, making it possible to include galaxies with all possible settings and positions on the celestial sphere in the study. Obtaining correct results, however, obliges one to take into account the Holmberg effect in the analysis, which consists of the fact that the measured, especially optical, ellipticity of the image of galaxies differs from the true ellipticity of the image [32; 33; 34; 35], and the fact that galaxies are flattened spheroids with the actual axis ratio depending on their morphological type. The method of analysis of the alignment of galaxies in clusters originally proposed in the papers [PERSON] (2012) and [PERSON] et al. (2019) [9; 27] has been greatly improved. The analysis of the spatial orientation of the galaxies from deprojection of their images required, in classical form, knowledge of morphological types of galaxies, which is rare with modern Kilo-Degree Surveys. Unfortunately, most of the currently available astronomical data do not provide information on the morphological types of galaxies. For this reason, research works, e.g., by [PERSON] [36], use the averaged values of the real ratio of the galaxies' axes. This solution may be insufficient in some cases, therefore, an alternative method is proposed [9; 37; 38; 39; 40], consisting of estimating the fraction of galaxies of a given morphological type. A new version of the method used for analyzing the orientation of galaxies in clusters, presented in the current work, makes it possible to carry out such an analysis, also in the case of the absence of information on their morphological types. We present the practical applications of this new variant of our method, as well as the implications of the results with reference to theories of galaxy formation.