A non-competitive antagonist is a type of insurmountable antagonist that may act in one of two ways: by binding to an allosteric site of the receptor, or by irreversibly binding to the active site of the receptor. The former meaning has been standardised by the IUPHAR, and is equivalent to the antagonist being called an allosteric antagonist.  While the mechanism of antagonism is different in both of these phenomena, they are both called "non-competitive" because the end-results of each are functionally very similar. Unlike competitive antagonists, which affect the amount of agonist necessary to achieve a maximal response but do not affect the magnitude of that maximal response, non-competitive antagonists reduce the magnitude of the maximum response that can be attained by any amount of agonist. This property earns them the name "non-competitive" because their effects cannot be negated, no matter how much agonist is present.  In functional assays of non-competitive antagonists, depression of the maximal response of agonist dose-response curves, and in some cases, rightward shifts, is produced. The rightward shift will occur as a result of a receptor reserve (also known as spare receptors) and inhibition of the agonist response will only occur when this reserve is depleted.
An antagonist that binds to the active site of a receptor is said to be "non-competitive" if the bond between the active site and the antagonist is irreversible or nearly so. This usage of the term "non-competitive" may not be ideal, however, since the term "irreversible competitive antagonism" may also be used to describe the same phenomenon without the potential for confusion with the second meaning of "non-competitive antagonism" discussed below.
The second form of "non-competitive antagonists" act at an allosteric site. These antagonists bind to a distinctly separate binding site from the agonist, exerting their action to that receptor via the other binding site. They  do not compete with agonists for binding at the active site. The bound antagonists may prevent conformational changes in the receptor required for receptor activation after the agonist binds.  Cyclothiazide has been shown to act as a reversible non-competitive antagonist of mGluR1 receptor. Another example of a non-competitive is phenoxybenzamine which binds irreversibly (with covalent bonds) to alpha-adrenergic receptors, which in turn reduces the fraction of available receptors and reduces the maximal effect that can be produced by the agonist.