diff --git a/Lib/fontTools/varLib/instancer/__init__.py b/Lib/fontTools/varLib/instancer/__init__.py
index d22cf49b64..a1787181ee 100644
--- a/Lib/fontTools/varLib/instancer/__init__.py
+++ b/Lib/fontTools/varLib/instancer/__init__.py
@@ -860,14 +860,24 @@ def instantiateAvar(varfont, axisLimits):
             )
             newMapping = {}
             for fromCoord, toCoord in mapping.items():
-
-                if fromCoord < axisRange.minimum or fromCoord > axisRange.maximum:
-                    continue
-                fromCoord = normalizeValue(fromCoord, (axisRange.minimum, 0, axisRange.maximum))
-
-                assert mappedMin <= toCoord <= mappedMax
-                toCoord = normalizeValue(toCoord, (mappedMin, 0, mappedMax))
-
+                if fromCoord < 0:
+                    if fromCoord < axisRange.minimum:
+                        continue
+                    else:
+                        fromCoord /= abs(axisRange.minimum)
+                elif fromCoord > 0:
+                    if fromCoord > axisRange.maximum:
+                        continue
+                    else:
+                        fromCoord /= axisRange.maximum
+                if toCoord < 0:
+                    assert mappedMin != 0
+                    assert toCoord >= mappedMin
+                    toCoord /= abs(mappedMin)
+                elif toCoord > 0:
+                    assert mappedMax != 0
+                    assert toCoord <= mappedMax
+                    toCoord /= mappedMax
                 fromCoord = floatToFixedToFloat(fromCoord, 14)
                 toCoord = floatToFixedToFloat(toCoord, 14)
                 newMapping[fromCoord] = toCoord