  This paper presents an innovative continuous linear finite element approach
to effectively solve biharmonic problems on surfaces. The key idea behind this
method lies in the strategic utilization of a surface gradient recovery
operator to compute the second-order surface derivative of a piecewise
continuous linear function defined on the approximate surface, as conventional
notions of second-order derivatives are not directly applicable in this
context. By incorporating appropriate stabilizations, we rigorously establish
the stability of the proposed formulation. Despite the presence of geometric
error, we provide optimal error estimates in both the energy norm and $L^2$
norm. Theoretical results are supported by numerical experiments.
