  There are discussed some modifications of n-th von Neumann-Jordan constant
considered by M. Kato, Y. Takahashi and K. Hashimoto. We study, among others,
upper, lower, upper modified and lower modified n-th von Neumann-Jordan
constant and relationships between them. There are characterized uniformly
non-l_{n}^{1} Banach spaces in terms of the upper modified n-th von
Neumann-Jordan constant. Moreover, this constant is calculated explicitly for
Lebesgue spaces L^{p} and l^{p} (1\leq p\leq oo).
