  A chain of magnetic atoms with non-collinear spin configuration on a
superconductor is a promising new system that can host Majorana Fermions (MFs).
In this study, we clarify that in the presence of MFs, an odd-frequency Cooper
pair is generated at the edge of the chain. Furthermore, it is revealed that
this feature is robust against the distance between magnetic atoms. We also
elucidate the close relationship between the pair amplitude of the
odd-frequency pair, the parity of the wave function, and the direction of the
MF spin. If Rashba-type spin-orbit coupling is included, MFs can be realized
even in a collinear alignment of magnetic atoms, $i.e.$, in a ferromagnetic or
anti-ferromagnetic chain on a superconductor. Then, the odd-frequency pairing
is generated at the edge, similar to the non-collinear case. Based on our
results, it can be concluded that the detection of the zero energy peak of the
local density of states by scanning tunneling microscopy at the edge of the
magnetic chain is strong evidence for the generation of odd-frequency pairing.
