'rejected completely' is correct and usable in standard written English.
You could use it to describe a situation in which an idea or proposal was not accepted at all. For example, "The board of directors completely rejected my proposal for a new system."
When they were delivered to the publisher, the blocks were rejected completely and Thornton was told that they should be completely recut.
American Ambassador Adlai E. Stevenson also rejected completely an uninspected test moratorium, which he called a "trap" that "we cannot afford to enter again".
Both streams are beginning to accept a negotiated solution something which until now the [Khatib's Syrian National] Coalition had rejected completely and utterly.
And there are new heroes, among them Senator David Norris, a towering icon of the equality fight in Ireland, who said he rejected completely the notion that a Yes vote was anything but completely in character for Ireland.
UV light (200 to 400 nm) was almost rejected completely by both films.
Yet for Erasmus himself, these traditional acts of external observance, while not necessarily practices to be rejected completely, were secondary matters and in many cases had been abused by grasping, corrupt clergymen as devices to exploit the simple, trusting faith of gullible believers.
Energy UK rejects completely any implication that the report was designed to alter the perception of supplier profit.
It is the decision to reject completely MPs' advice to amend rules, passed in 2011, for drawing new boundaries.
Some computer simulations results are included to show controller robustness to reject completely unknown chaotic load torque disturbances and parametric uncertainty, as well as effectiveness of the differentiation scheme of signals.
He opposed this tendency toward transcendental idealism in Formal and Transcendental Logic but refused to reject, completely, phenomenology (Obras, 5: 545).
To reject completely any notion of collective guilt is to bear down all the harder on the idea of individual responsibility.
