The 2015 Paris Agreement sets out that rapid reductions in greenhouse gas (GHG) emissions are needed to keep global warming to safe levels. A new approach (known as GWP*) has been suggested to compare contributions of long- and short-lived GHGs, providing a close link between cumulative CO2-equivalent emissions and total warming. However, comparison factors for non-CO2 GHGs under the GWP* metric depend on past emissions, and hence raise questions of equity and fairness when applied at any but the global level. The use of GWP* would put most developing countries at a disadvantage compared to developed countries, because when using GWP* countries with high historical emissions of short-lived GHGs are exempted from accounting for avoidable future warming that is caused by sustaining these emissions. We show that when various established equity or fairness criteria are applied to GWP* (defined here as eGWP*), perceived national non-CO2 emissions vary by more than an order of magnitude, particularly in countries with high methane emissions like New Zealand. We show that national emission estimates that use GWP* are very sensitive to arbitrary choices made by countries and therewith facilitate the creation of loopholes when CO2-equivalent emissions based on the GWP* concept are traded between countries that use different approaches. In light of such equity-dependent accounting differences, GHG metrics like GWP* should only be used at the global level. A common, transparent and equity-neutral accounting metric is vital for the Paris Agreement's effectiveness and its environmental integrity.