  In this note we formulate and prove a version of Cartan decomposition for
holomorphic loop groups, similar to Cartan decomposition for $p$-adic loop
groups, discussed proved by Garland (and later by the authors by geometric
mathods). The main technical tool that we use is the (well-known)
interpretation of twisted conjugacy classes in the holomorphic loop group in
terms of principal holomorphic bundles on an elliptic curve.
