If the probability of a quadrilateral being a square is 0.4, then the probability of the quadrilateral not being a square is 0.6.

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The correct option is $\mathbf{C}$ (0.6).

Let $P(S)$ represent the probability of a quadrilateral being a square.

Let $P(S')$ represent the probability of a quadrilateral not being a square.

Since $P(S)$ and $P(S')$ are complementary events, their probabilities add up to 1: $$P(S) + P(S') = 1$$

Given: $$P(S) = 0.4$$

Substitute this value into the equation: $$0.4 + P(S') = 1$$

Solve for $P(S')$: $$P(S') = 1 - 0.4$$ $$P(S') = 0.6$$

Thus, the probability of a quadrilateral not being a square is $0.6$.