  We have discovered two unconstrained forms of free Lagrangian for continuous
spin(CS) theory in arbitrary flat spacetime dimension for bosonic case. These
Lagrangians, unlike that by Schuster and Toro, do not include delta functions
and are conventional. The first form consists of five kinds of totally
symmetric helicity fields and one kind of gauge parameter. By introducing
auxiliary creation and annihilation operators, each is combined into a state
vector in Fock space, including all ranks one by one. The Lagrangian imposes no
constraints, such as trace conditions, on these fields or the gauge parameter
field. Additionally, the Lagrangian does not contain higher-order derivative
terms. In the limit as CS parameter $\mu$ approaches zero, it naturally
reproduces a Lagrangian for helicity fields in higher spin(HS) theory, known as
unconstrained quartet formulation. Permitting third-order derivatives, we also
obtain the second unconstrained form of Lagrangian that can be written in terms
of three kinds of fields, including $\mu$, similar to the formulation by
Francia and Sagnotti. Partial gauge fixing and partial use of equations of
motion(EOM) on this Lagrangian yield a Fronsdal-like Lagrangian with a single
double-traceless field, including $\mu$. By imposing further gauge fixing on
the field in the EOM with respect to divergence and trace, we confirm the
reproduction of the modified Wigner equations already known in literature.
