This paper proposes a new method for distributing the European Regional Development Fund (ERDF) budget, addressing the limitations of existing egalitarian approaches. The current approach, using the Constrained Equal Losses (CEL) rule, while effective in reducing inequality, may result in some regions receiving no funds. The authors introduce the CELmin rule, which combines egalitarian fund division with egalitarian loss division, guaranteeing a minimum allocation to each region. The CELmin rule is axiomatically analyzed and applied to the ERDF problem, demonstrating its effectiveness in promoting convergence while ensuring all regions receive funding.