Unipolar stepper - one direction

Is this sketch the most direct method to run a unipolar stepper in one direction? Using the stepper library would seem to involve less code but I haven't been successful using it for a single direction.

int motorPin1 = 8;
int motorPin2 = 9;
int motorPin3 = 10;
int motorPin4 = 11;
int delayTime = 10;

void setup() {
pinMode(motorPin1, OUTPUT);
pinMode(motorPin2, OUTPUT);
pinMode(motorPin3, OUTPUT);
pinMode(motorPin4, OUTPUT);
}

void loop() {
digitalWrite(motorPin1, HIGH);
digitalWrite(motorPin2, LOW);
digitalWrite(motorPin3, LOW);
digitalWrite(motorPin4, LOW);
delay(delayTime);
digitalWrite(motorPin1, LOW);
digitalWrite(motorPin2, HIGH);
digitalWrite(motorPin3, LOW);
digitalWrite(motorPin4, LOW);
delay(delayTime);
digitalWrite(motorPin1, LOW);
digitalWrite(motorPin2, LOW);
digitalWrite(motorPin3, HIGH);
digitalWrite(motorPin4, LOW);
delay(delayTime);
digitalWrite(motorPin1, LOW);
digitalWrite(motorPin2, LOW);
digitalWrite(motorPin3, LOW);
digitalWrite(motorPin4, HIGH);
delay(delayTime);
}

Your code is OK.
Maybe play with the delay.
Do you have a common ground?
Your programming technique will improve as you become more knowledgeable.

What components are you using?
Show us how your motor is wired up, a schematic, a picture.

I should have mentioned the ULN2003 to drive the motors. The sketch above I assume will run the stepper without this chip or the library. Fortunately, I adapted a much shorter sketch which works well. Thanks.