Final answer:
The function that should not be assigned to the company's accounting department for effective internal control is signing payroll checks, as it goes against the segregation of duties principle.
Step-by-step explanation:
For effective internal control, the function that should not be assigned to the company's accounting department is C. Signing payroll checks. This practice is counter to the principle of segregation of duties, which aims to reduce the risk of fraud and errors. This principle dictates that the responsibility for authorizing transactions (in this case, signing payroll checks) should be separate from the responsibility for recording or reporting the transactions. By having a separation of tasks, companies can create a system of checks and balances that increases accuracy and reduces the likelihood of unauthorized or fraudulent activities.