  Our main result is a monogamy inequality satisfied by the entanglement of a
focus qubit (one-tangle) in a four-qubit pure state and entanglement of
subsystems. Analytical relations between three-tangles of three-qubit marginal
states, two-tangles of two-qubit marginal states and unitary invariants of
four-qubit pure state are used to obtain the inequality. The contribution of
three-tangle to one-tangle is found to be half of that suggested by a simple
extension of entanglement monogamy relation for three qubits. On the other
hand, an additional contribution due to a two-qubit invariant which is a
function of three-way correlations is found. We also show that four-qubit
monogamy inequality conjecture of ref. [PRL 113, 110501 (2014)] in which
three-tangles are raised to the power (3/2), does not estimate the residual
correlations, correctly. A lower bound on residual four-qubit correlations is
obtained.
