Redundant assets give rise to peculiar portfolios, called `link portfolios,' under portfolio constraints. Link portfolios are jointly spanned by constrained null-income portfolios and form a linear subspace. The paper provides a general methodology for showing the existence of equilibrium under portfolio constraints by building two theoretical pillars to deal with link portfolios. The two pillars consist of the fundamental theorem of portfolio decomposition and the allocational equivalence between the original economy and the artificial economy built from projecting away link portfolios from the portfolio constraints. Investigating the existence of equilibrium in constrained financial markets boils down to finding a sufficient condition for the fundamental theorem of portfolio constraints to hold. The sufficient condition of the paper is general enough to encompass other sufficient conditions of the literature.