The pseudocode for the L₁-PCA* algorithm is given next.

Algorithm L1-PCA*
Given a data matrix $X\in {\mathbb{R}}^{n\times m}$ with full column rank.
1: Set Xm = X; set Vm+1 = I; set (Ij*)m+1 = I.	/* Initialization. */
2: for (k = m; k > 1; k = k − 1) do
3: Set $j^{\ast }=\stackrel{\mathrm{argmin}}{j}{R}_j\left(X^k\right)$ and βk = β* using the Algorithm for finding a L1-norm best-fit  subspace of dimension m − 1.	/* Find the best-fitting L1 subspace among subspaces derived with each variable j as the dependent variable. */
4: Set Zk = (Xk)((Ij*)k)T.	/* Project points into a (k − 1)-dimensional subspace. */
5: Calculate the SVD of Zk, Zk = UΛVT , and set Vk to be equal to the (k − 1) columns of V corresponding to the largest values in the diagonal matrix Λ.	/* Find a basis for the (k − 1)-dimensional subspace. */
6: Set ${\alpha }^k=\left({\prod }_{\ell =m+1}^{k+1}{V}^{\ell }\right){\beta }^k∕{\mid \mid {\beta }^k\mid \mid }_2$	/* Calculate the kth principal component. */
7: Set X(k−1) = ZkVk.	/* Calculate the projected points in terms of the new basis. */
8: end for
9: Set ${\alpha }^1={\prod }_{\ell =m+1}^2{V}^{\ell }$.	/* Calculate the first principal component. */

Notes on L₁-PCA*