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For a fusion Banach frame $(\{G_n,v_n\},S)$ for a Banach space $E$, if $(\{v_n^{*}\left(E^{*}\right),v_n^{*}\},T)$ is a fusion Banach frame for $E^{*}$, then $(\{G_n,v_n\},S;\{v_n^{*}\left(E^{*}\right),v_n^{*}\},T)$ is called a fusion bi-Banach frame for $E$. It is proved that if $E$ has an atomic decomposition, then $E$ also has a fusion bi-Banach frame. Also, a sufficient condition for the existence of a fusion bi-Banach frame is given. Finally, a characterization of fusion bi-Banach frames is given.

A stronger version of the notion of frame in Banach space called Strong Retro Banach frame (SRBF) is defined and studied. It has been proved that if $𝒳$ is a Banach space such that ${𝒳}^{*}$ has a SRBF, then $𝒳$ has a Bi-Banach frame with some geometric property. Also, it has been proved that if a Banach space $𝒳$ has an approximative Schauder frame, then ${𝒳}^{*}$ has a SRBF. Finally, the existence of a non-linear SRBF in the conjugate of a separable Banach space has been proved.