Note to Macbeth, Act 1, Scene 4, lines 48: "The Prince of Cumberland!"

After King Duncan announces that his eldest son Malcolm is to be heir to the throne, Macbeth exclaims,

The Prince of Cumberland! that is a step
On which I must fall down, or else o'erleap,
For in my way it lies.

However, Macbeth never does make a plan to get Malcolm out of the way, and after King Duncan is murdered, Malcolm flees because he thinks he may be next to be killed. Afterwards Macbeth promotes the idea that Malcolm plotted his own father's death, then ran away, which showed his guilt, but this whole idea seems to be an after-the-fact spin which no one believes.

In addition, some commentators have pointed out that in the Scotland of Macbeth's time (not Shakespeare's) the eldest son of a king was not automatically heir apparent; other persons of royal lineage (such as Macbeth, who is King Duncan's first cousin) could hope that the nobility would elect one of them to the throne. This may be reflected in the previous scene when Macbeth told himself that "chance may crown me, / Without my stir." However, Macbeth does not mention any of this; he does not make a case that King Duncan is making an unacceptable change to Scottish tradition.