The structure of (La1-xSrx)4CuO10 (x=0.1429) has been reexamined by neutron powder diffraction techniques. The results confirm the structural model based on the X-ray powder diffraction data. The general structural features of this material are similar to those of the other three-dimensional oxygen-deficient perovskites BaLa4Cu5O14-delta, La1-xSrx)8Cu8O20-delta (0.16 less-than-or-equal-to x less-than-or-equal-to 0.24) and La2Sr6Cu8O18-delta; in particular the oxygen vacancies in the basal plane are ordered along [001]. The framework of [Cu4O10] consists of one type of comer-shared CuO5 groups. X-ray powder diffraction and thermal analysis investigations showed that the orthorhombic phase (La1-xSrx)4Cu4O10 (x=0.1429) is thermodynamically stable at low temperature (<500-degrees-C), although it can only be prepared above 1020-degrees-C in oxygen. The phase transition from orthorhombic (La1-xSrx)4Cu4O10 to tetragonal (La1-xSrx)8 Cu8O20 (x=0.1429) above 500-degrees-C is slow and occurs over a wide temperature range, characteristic of a second-order transition.