  This paper presents a new matrix-infinite-product-form (MIP-form) solution
for the stationary distribution in upper block-Hessenberg Markov chains
(UBH-MCs). The existing MIP-form solution (Masuyama, Queueing Syst., Vol. 92,
2019, pp. 173--200) requires a certain parameter set that satisfies both a
Foster-Lyapunov drift condition and a convergence condition. In contrast, the
new MIP-form solution requires no such parameter sets and no other conditions.
The new MIP-form solution also has "quasi-algorithmic constructibility", which
is a newly introduced feature of being constructed by iterating infinitely many
times a recursive procedure of finite complexity per iteration. This feature is
not found in the other solutions for the stationary distribution in UBH-MCs.
