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Gives a flat 4% per level increase to your personal standing with unfriendly NPC factions/corps. If you have (for example) good standings with Creodron corp, but bad standings with the Gallente faction, then your Creodron standings are boosted by 'either' Diplomacy 'or' Connections, whichever is trained higher. Also, this will help keep the Gallente police from coming after you when you enter their space.
Diplomacy Mutator: 0.4
The in-game description is misleading; it says "0.4 bonus" when it really means "4% bonus" as said above, the same as Connections. The usual standing gain formula applies:
Standing + (10 - Standing) * (0.04 * SkillLevel)
Except, in this case, Standing is negative. (E.g. for an original standing of -5.76 and Level II Diplomacy, you end up with -5.76 + (10 + 5.75) * 0.08 = -4.5.)