  We advance previous studies on decomposed Richelot isogenies
(Katsura--Takashima (ANTS 2020) and Katsura (ArXiv 2021)) which are useful for
analysing superspecial Richelot isogeny graphs in cryptography. We first give a
characterization of decomposed Richelot isogenies between Jacobian varieties of
hyperelliptic curves of any genus. We then define generalized Howe curves, and
present two theorems on their relationships with decomposed Richelot isogenies.
We also give new examples including a non-hyperelliptic (resp.\,hyperelliptic)
generalized Howe curve of genus 5 (resp.\,of genus 4).
