We present the chemical abundances of 57 metal-poor ([Fe/H] < -1) stars that are likely constituents of the outer stellar halo in the Milky Way. Almost all of the sample stars have an orbit reaching a maximum vertical distance (Z(max)) of > 5 kpc above and below the Galactic plane. High-resolution (R similar to 50000-55000), high signal-to-noise (S/N > 100) spectra for the sample stars obtained with Subaru/HDS were used to derive the chemical abundances of Na, Mg, Ca, Ti, Cr, Mn. Fe, Ni, Zn, Y, and Ba with an LTE abundance analysis code. The resulting abundance data were combined with those presented in the literature that mostly targeted at smaller Z(max) stars, and both data were used to investigate any systematic trends in detailed abundance patterns depending on their kinematics. It was shown that, in the metallicity range of 2 < [Fe/H] < 1, the [Mg/Fe] ratios for stars with Z(max) > 5 kpc are systematically lower (similar to 0.1 dex) than those with a smaller Z(max). For this metallicity range, a modest degree of depression in the [Si/Fe] and the [Ca/Fe] ratios was also observed. This result of lower [alpha/Fe] for the assumed outer halo stars is consistent with previous studies that found a signature of lower [alpha/Fe] ratios for stars with extreme kinematics. The distribution of the [Mg/Fe] ratios for the outer halo stars partly overlaps with that for stars belonging to the Milky Way dwarf satellites in the metallicity interval of -2 < [Fe/H] < -1 and spans a range intermediate between the distributions for the inner halo stars and the stars belonging to the satellites. Our results confirm the inhomogeneous nature of the chemical abundances within the Milky Way stellar halo, depending on the kinematic properties of the constituent stars, as suggested by earlier studies. Possible implications for the formation of the Milky Way halo and its relevance to the suggested dual nature of the halo are discussed.