Context. Eigenvector 1 (EV1) is the formal parameter which allows the introduction of some order in the properties of the unobscured type 1 active galaxies. Aims. We aim to understand the nature of this parameter by analyzing the most extreme examples of quasars with the highest possible values of the corresponding eigenvalues R_Fe. Methods. We selected the appropriate sources from the Sloan Digital Sky Survey (SDSS) and performed detailed modeling, including various templates for the Fe II pseudo-continuum and the starlight contribution to the spectrum. Results. Out of 27 sources with R_Fe larger than 1.3 and with the measurement errors smaller than 20% selected from the SDSS quasar catalog, only six sources were confirmed to have a high value of R_Fe, defined as being above 1.3. All other sources have an R_Fe of approximately 1. Three of the high R_Fe objects have a very narrow Hβ line, below 2100 km s⁻¹ but three sources have broad lines, above 4500 km s⁻¹, that do not seem to form a uniform group, differing considerably in black hole mass and Eddington ratio; they simply have a very similar EW([OIII]5007) line. Therefore, the interpretation of the EV1 remains an open issue.