diff --git a/src/main/java/com/github/f4b6a3/ulid/Ulid.java b/src/main/java/com/github/f4b6a3/ulid/Ulid.java
index dd8f819..1c655e1 100644
--- a/src/main/java/com/github/f4b6a3/ulid/Ulid.java
+++ b/src/main/java/com/github/f4b6a3/ulid/Ulid.java
@@ -149,10 +149,14 @@ public final class Ulid implements Serializable, Comparable<Ulid> {
 	/**
 	 * Creates a new ULID.
 	 * <p>
-	 * Time parameter is the number of milliseconds since 1970-01-01 (Unix epoch).
-	 * It must be a positive number not larger than 2^48-1.
+	 * The time parameter is the number of milliseconds since 1970-01-01, also known
+	 * as Unix epoch. It must be a positive number not larger than 2^48-1.
 	 * <p>
-	 * Random parameter must be an array of 10 bytes.
+	 * The random parameter must be an arbitrary array of 10 bytes.
+	 * <p>
+	 * Note: ULIDs cannot be composed of dates before 1970-01-01, as their embedded
+	 * timestamp is internally treated as an unsigned integer, i.e., it can only
+	 * represent the set of natural numbers including zero, up to 2^48-1.
 	 * 
 	 * @param time   the number of milliseconds since 1970-01-01
 	 * @param random an array of 10 bytes
diff --git a/src/main/java/com/github/f4b6a3/ulid/UlidFactory.java b/src/main/java/com/github/f4b6a3/ulid/UlidFactory.java
index 9ec5e97..256e261 100644
--- a/src/main/java/com/github/f4b6a3/ulid/UlidFactory.java
+++ b/src/main/java/com/github/f4b6a3/ulid/UlidFactory.java
@@ -360,7 +360,8 @@ public final class UlidFactory {
 		}
 
 		void initialize(LongSupplier timeFunction) {
-			this.lastUlid = new Ulid(timeFunction.getAsLong(), this.random.nextBytes(Ulid.RANDOM_BYTES));
+			// initialize the factory with the instant 1970-01-01 00:00:00.000 UTC
+			this.lastUlid = new Ulid(0L, this.random.nextBytes(Ulid.RANDOM_BYTES));
 		}
 
 		@Override
diff --git a/src/test/java/com/github/f4b6a3/ulid/UlidFactoryMonotonicTest.java b/src/test/java/com/github/f4b6a3/ulid/UlidFactoryMonotonicTest.java
index cd93a9d..ee80ee3 100644
--- a/src/test/java/com/github/f4b6a3/ulid/UlidFactoryMonotonicTest.java
+++ b/src/test/java/com/github/f4b6a3/ulid/UlidFactoryMonotonicTest.java
@@ -39,8 +39,7 @@ public class UlidFactoryMonotonicTest extends UlidFactoryTest {
 
 		long diff = UlidFactory.MonotonicFunction.CLOCK_DRIFT_TOLERANCE;
 		long time = Instant.parse("2021-12-31T23:59:59.000Z").toEpochMilli();
-		long times[] = { /* init */ 0L, time + 0, time + 1, time + 2, time + 3, time + 4 - diff, time + 5 - diff,
-				time + 6 - diff };
+		long times[] = { time + 0, time + 1, time + 2, time + 3, time + 4 - diff, time + 5 - diff, time + 6 - diff };
 
 		Clock clock = new Clock() {
 			private int i;
@@ -113,8 +112,11 @@ public class UlidFactoryMonotonicTest extends UlidFactoryTest {
 	@Test
 	public void testGetMonotonicUlidAfterLeapSecond() {
 
+		// The best article about leap seconds:
+		// (Unfortunately it can't be translated)
+		// https://ntp.br/conteudo/artigo-leap-second/
 		long time = Instant.parse("2021-12-31T23:59:59.000Z").toEpochMilli();
-		long leap = time - 1000; // simulate a leap second
+		long leap = time - 1000; // moving the clock hands 1 second backwards
 		long times[] = { time, leap };
 
 		Clock clock = new Clock() {
@@ -144,28 +146,26 @@ public class UlidFactoryMonotonicTest extends UlidFactoryTest {
 		LongSupplier randomFunction = () -> 0;
 		UlidFactory factory = UlidFactory.newMonotonicInstance(randomFunction, clock);
 
+		// the clock moved normally
 		Ulid ulid1 = factory.create();
-		Ulid ulid2 = factory.create();
-
 		long t1 = ulid1.getTime();
-		long t2 = ulid2.getTime(); // leap second
-
 		long r1 = ulid1.getLeastSignificantBits();
-		long r2 = ulid2.getLeastSignificantBits(); // leap second
-
 		assertEquals(time, t1);
-		assertEquals(time, t2); // leap second
-
-		assertEquals(1, r1);
-		assertEquals(2, r2);
+		assertEquals(0, r1);
 
+		// the clock moved backwards
+		Ulid ulid2 = factory.create();
+		long t2 = ulid2.getTime();
+		long r2 = ulid2.getLeastSignificantBits();
+		assertEquals(time, t2); // should freeze
+		assertEquals(1, r2); // should increment
 	}
 
 	@Test
 	public void testGetMonotonicUlidAfterRandomBitsOverflowFollowedByTimeBitsIncrement() {
 
 		long time = Instant.parse("2021-12-31T23:59:59.999Z").toEpochMilli();
-		long times[] = { /* init */ 0L, time + 1, time + 2, time + 3, time, time, time };
+		long times[] = { time + 1, time + 2, time + 3, time, time, time };
 
 		Clock clock = new Clock() {
 			private int i;
@@ -194,8 +194,6 @@ public class UlidFactoryMonotonicTest extends UlidFactoryTest {
 		LongSupplier randomSupplier = () -> 0xffffffffffffffffL;
 		UlidFactory factory = UlidFactory.newMonotonicInstance(randomSupplier, clock);
 
-		// System.out.println("time: " + time); // 1640995199999
-
 		Ulid ulid1 = factory.create();
 		Ulid ulid2 = factory.create();
 		Ulid ulid3 = factory.create();