Whereas modern automated blood cell analyzers measure the volume of individual red blood cells (RBCs), leading to four RBC indices (mean corpuscular volume, MCV; mean corpuscular hemoglobin, MCH; mean corpuscular hemoglobin concentration, MCHC; red cell distribution width, and RDW), the RBC shape has not been assessed by clinical screening tools. We applied the scanning flow cytometer (SFC) for complete characterization of intact RBC morphology in terms of diameter, maximal and minimal thicknesses, volume, surface area, sphericity index, spontaneous curvature, hemoglobin concentration, and content. The above-mentioned individual RBC characteristics were measured without fluorescent markers and other chemicals by a SFC equipped only with 660 nm laser for RBC illumination and single detector for measurement of angle-resolved light scattering. The distributions over all RBC characteristics were constructed and processed statistically to form the novel 31 RBC indices for 22 donor samples. Our results confirm the possibility of precise, label-free, enhanced morphological analysis of individual intact RBCs with compact single-detector flow cytometer. Detailed characterization of RBCs with high statistics and precision can be used to increase the value of screening examinations and to reveal pathologies accompanied by abnormality of RBC shape.