unrechtmäßig
unlawful
Violating the law, a regulation, or a right; not legal or legitimate.
Die unrechtmäßige Kündigung wurde vor Gericht angefochten.
The unlawful dismissal was challenged in court.

unlawful
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unlawful
Violating the law, a regulation, or a right; not legal or legitimate.
Die unrechtmäßige Kündigung wurde vor Gericht angefochten.
The unlawful dismissal was challenged in court.

The word is clearly structured: the prefix 'un-' negates the word 'rechtmäßig' (lawful). 'Rechtmäßig' itself means 'in accordance with the law,' so fitting the law. 'Unrechtmäßig' (unlawful) therefore literally means 'not in accordance with the law.'
Er hat sich das Geld auf unrechtmäßige Weise beschafft.
He obtained the money in an unlawful way.
'Unrechtmäßig' (unlawful) is a formal word used mainly in written language, in legal or administrative contexts. It sounds very official.
Das Gericht erklärte die Gebührenerhöhung für unrechtmäßig.
The court declared the fee increase unlawful.
This adjective is often combined with nouns from the legal or economic sphere. Typical phrases are 'unrechtmäßiger Besitz' (unlawful possession), 'unrechtmäßige Bereicherung' (unjust enrichment), or 'unrechtmäßige Nutzung' (unlawful use).
Der unrechtmäßige Besitzer des Grundstücks musste es zurückgeben.
The unlawful owner of the property had to return it.
right
'von Rechts wegen' (by right) and 'unrechtmäßig' are opposites when it comes to law and legal rights. 'von Rechts wegen' means that something is based on a right or is lawful. 'unrechtmäßig', on the other hand, means that something violates a law, a regulation, or a right. If you want to say that something is permitted or justified, 'von Rechts wegen' fits. If something is not legal or not legitimate, 'unrechtmäßig' fits.

Die Firma hat die Daten unrechtmäßig gespeichert.
The company stored the data unlawfully.
Von Rechts wegen steht ihr eine Entschädigung zu.
By right, she is entitled to compensation.