  The conditional copula model arises when the dependence between random
variables is influenced by another covariate. Despite its importance in
modelling complex dependence structures, there are very few fully nonparametric
approaches to estimate the conditional copula function. In the bivariate
setting, the only nonparametric estimator for the conditional copula is based
on Sklar's Theorem and proposed by Gijbels \textit{et al.} (2011). In this
paper, we propose an alternative nonparametric approach %based on functional
principal component analysis. We to construct an estimator for the bivariate
conditional copula from the Karhunen-Lo\`eve representation of a suitably
defined conditional copula process. We establish its consistency and weak
convergence to a limit Gaussian process with explicit covariance function.
