The γ′ lattice parameter aγ′ and the α angle defining the primary crystal orientation of the single-crystalline cored turbine blades made of CMSX-4 superalloy were measured in the areas located near the selector situated asymmetrically, considering the top view of the blade. The distributions of the aγ′ and the α angle were determined along the lines parallel to the vertical blade axis Z using X-ray diffraction methods. The relations between changes in the aγ′(Z) and α(Z) were analyzed on the Z levels where the shape of the blade’s cross-section changes. For the first time, the local increase in aγ′(Z) was found near the root–airfoil connection level and near certain other root levels, which is related to the change in blade section shapes on such levels. The local extremes in α(Z), representing the dendrite bend, were observed at these levels. The increase in the aγ′(Z) with the local bending of dendrites was discussed concerning the local redistribution of alloying elements and local residual stresses of the γ-dendrites. For the first time, a method of analyzing the local bending of the dendrites was proposed by studying the behavior of the α(Z). The presented results concern the first stage of the research covering areas relatively close to the selector, considering the top view of the blades. The second stage will include the analysis of the areas of the blade localized at a longer distance from the selector.