The increasing ubiquity of multivariate functional data (MFD) requires methods that can properly detect outliers within such data, where a sample corresponds to $p>1$ parameters observed with respect to (w.r.t) a continuous variable (extit{e.g.} time). We improve the outlier detection in MFD by adopting a geometric view on the data space while combining the new data representation with state-of-the-art outlier detection algorithms. The geometric representation of MFD as paths in the $p$-dimensional Euclidean space enables to implicitly take into account the correlation w.r.t the continuous variable between the parameters. We experimentally show that our method is robust to various rates of outliers in the training set when fitting the outlier detection model and can detect outliers which are not detected by standard algorithms.