A color space is a three-dimensional representation of all the possible color percepts. The CIE 1976 L*a*b* is one of the most widely used object color spaces. In CIELAB, lightness L* is limited between 0 and 100, while a* and b* coordinates have no fixed boundaries. The outer boundaries of CIELAB have been previously calculated using theoretical object spectral reflectance functions and the CIE 1931 and 1964 observers under the CIE standard illuminants D50 and D65. However, natural and manufactured objects reflect light smoothly as opposed to theoretical spectral reflectance functions. Here, data generated from a linear optimization method are analyzed to re-evaluate the outer boundaries of the CIELAB. The color appearance of 99 test color samples under theoretical test spectra has been calculated in the CIELAB using CIE 1931 standard observer. The lightness L* boundary ranged between 6 and 97, redness-greenness a* boundary ranged between -199 and 270, and yellowness-blueness b* boundary ranged between -74 and 161. The boundary in the direction of positive b* (yellowness) was close to the previous findings. While the positive a* (redness) boundary exceeded previously known limits, the negative a* (greenness) and b* (blueness) boundaries were lower than the previously calculated CIELAB boundaries. The boundaries found here are dependent on the color samples used here and the spectral shape of the test light sources. Irregular spectral shapes and more saturated color samples can result in extended boundaries at the expense of computational time and power.