diff --git a/src/main/java/mil/nga/gars/GARS.java b/src/main/java/mil/nga/gars/GARS.java
index 4d9e076..38b05d1 100644
--- a/src/main/java/mil/nga/gars/GARS.java
+++ b/src/main/java/mil/nga/gars/GARS.java
@@ -315,31 +315,34 @@ public static GARS from(Point point) {
 
 		// Normalize the longitude if needed
 		GeometryUtils.normalizeWGS84(point);
+		double longitude = point.getLongitude();
+		if (longitude >= GARSConstants.MAX_LON) {
+			// 180 is the same meridian as -180, in band 001
+			longitude -= 360.0;
+		}
 
-		double lon = GARSUtils.getLongitudeDecimalBand(point.getLongitude());
-		double lat = GARSUtils.getLatitudeDecimalBandValue(point.getLatitude());
+		// Index of the 5 minute cell, counted from 180 W and 90 S. Multiply
+		// before adding the offset so that values on a cell boundary land in
+		// the cell they start (scaling the band fractions in steps let
+		// rounding put them in the cell below or to the left). The top row
+		// includes latitude 90.
+		int lonIndex = (int) Math.floor(longitude * 12.0) + 180 * 12;
+		int latIndex = (int) Math.floor(point.getLatitude() * 12.0) + 90 * 12;
+		lonIndex = Math.max(0, Math.min(lonIndex, 360 * 12 - 1));
+		latIndex = Math.max(0, Math.min(latIndex, 180 * 12 - 1));
 
-		int lonInt = (int) lon;
-		int latInt = (int) lat;
+		int lonInt = lonIndex / 6 + 1;
+		int latInt = latIndex / 6 + 1;
 
 		String latBand = GARSUtils.bandLetters(latInt);
 
-		double lonDecimal = lon - lonInt;
-		double latDecimal = lat - latInt;
-
-		double quadrantColumn = lonDecimal * 2.0;
-		double quadrantRow = latDecimal * 2.0;
-
-		int quadrantColumnInt = (int) quadrantColumn;
-		int quadrantRowInt = (int) quadrantRow;
+		int quadrantColumnInt = (lonIndex % 6) / 3;
+		int quadrantRowInt = (latIndex % 6) / 3;
 
 		int quadrant = GARSUtils.quadrant(quadrantColumnInt, quadrantRowInt);
 
-		lonDecimal = quadrantColumn - quadrantColumnInt;
-		latDecimal = quadrantRow - quadrantRowInt;
-
-		int keypadColumn = (int) (lonDecimal * 3.0);
-		int keypadRow = (int) (latDecimal * 3.0);
+		int keypadColumn = lonIndex % 3;
+		int keypadRow = latIndex % 3;
 
 		int keypad = GARSUtils.keypad(keypadColumn, keypadRow);
 
diff --git a/src/test/java/mil/nga/gars/GARSTest.java b/src/test/java/mil/nga/gars/GARSTest.java
index e4fb015..7256041 100644
--- a/src/test/java/mil/nga/gars/GARSTest.java
+++ b/src/test/java/mil/nga/gars/GARSTest.java
@@ -290,7 +290,9 @@ public void testPointBounds() {
 
 		// Max latitude tests
 
-		String gars = "462RA49";
+		// Latitude 90 is in the top band, QZ (there is no band RA, and
+		// parse() rejects it)
+		String gars = "462QZ23";
 		String gars2 = "462QZ26";
 		double longitude = 50.920338;
 		double latitudeBelow = 89.9;
@@ -497,4 +499,45 @@ private void testCoordinate(Point point, String value)
 
 	}
 
+	/**
+	 * Test points on the antimeridian, at the north pole, and on whole
+	 * minute cell boundaries
+	 * 
+	 * @throws ParseException
+	 *             upon failure to parse
+	 */
+	@Test
+	public void testCellBoundaries() throws ParseException {
+
+		// 180 is the same meridian as -180; latitude 90 is in the top row.
+		// These used to give 721HN37 and 361RA37, which parse() rejects.
+		assertEquals("001HN37", GARS.from(180, 0).coordinate());
+		assertEquals("361QZ11", GARS.from(0, 90).coordinate());
+		assertEquals("001QZ11", GARS.from(180, 90).coordinate());
+		assertEquals("720QZ23", GARS.from(179.9999999, 89.9999999).coordinate());
+		GARS.parse(GARS.from(180, 0).coordinate());
+		GARS.parse(GARS.from(0, 90).coordinate());
+
+		// A point on a 5 minute boundary is in the cell it starts
+		// (10 05' E 10 05' N used to give 381JJ38, the cell to the south)
+		assertEquals("381JJ35", GARS.from(10 + 5 / 60.0, 10 + 5 / 60.0).coordinate());
+		assertEquals("340GR23",
+				GARS.from(-(10 + 5 / 60.0), -(10 + 5 / 60.0)).coordinate());
+
+		for (int i = 0; i < 360 * 12; i += 7) {
+			for (int j = 0; j < 180 * 12; j += 5) {
+				int lonMinutes = i * 5 - 180 * 60;
+				int latMinutes = j * 5 - 90 * 60;
+				double lon = Math.signum(lonMinutes) * (Math.abs(lonMinutes) / 60
+						+ (Math.abs(lonMinutes) % 60) / 60.0);
+				double lat = Math.signum(latMinutes) * (Math.abs(latMinutes) / 60
+						+ (Math.abs(latMinutes) % 60) / 60.0);
+				Point southwest = GARS.from(lon, lat).toPoint();
+				assertEquals(lon, southwest.getLongitude(), 1e-9);
+				assertEquals(lat, southwest.getLatitude(), 1e-9);
+			}
+		}
+
+	}
+
 }