diff --git a/src/Zip Tests/Streams.cs b/src/Zip Tests/Streams.cs
index a4993ae..ba67847 100644
--- a/src/Zip Tests/Streams.cs	
+++ b/src/Zip Tests/Streams.cs	
@@ -210,6 +210,29 @@ public void ReadZip_OpenReader()
         }
 
 
+        // Read a file consisting of a 16 byte header and one embedded zip archive
+        [TestMethod]
+        public void ReadZip_WithOffset()
+        {
+            string filename = Path.Combine(CurrentDir, "zips\\offset.bin");
+            string header = null;
+            int entries = 0;
+
+            using (FileStream fs = new FileStream(filename, FileMode.Open, FileAccess.Read, FileShare.Read))
+            using (BinaryReader br = new BinaryReader(fs))
+            {
+                header = Encoding.ASCII.GetString(br.ReadBytes(16));
+                using (ZipFile zip = ZipFile.Read(fs))
+                {
+                    entries = zip.Entries.Count;
+                }
+            }
+
+            Assert.AreEqual<string>("16-byte header\0\0", header, "Error reading header");
+            Assert.AreEqual<int>(1, entries, "Error reading embedded zip file");
+        }
+
+
         [TestMethod]
         public void ZOS_Create_WithComment_wi10339()
         {
diff --git a/src/Zip Tests/Zip Tests.csproj b/src/Zip Tests/Zip Tests.csproj
index 8c7be4b..5386b2c 100644
--- a/src/Zip Tests/Zip Tests.csproj	
+++ b/src/Zip Tests/Zip Tests.csproj	
@@ -165,6 +165,9 @@
     <Content Include="zips\relative-paths-in-subdir-outside.zip">
       <CopyToOutputDirectory>Always</CopyToOutputDirectory>
     </Content>
+    <None Include="zips\offset.bin">
+      <CopyToOutputDirectory>Always</CopyToOutputDirectory>
+    </None>
   </ItemGroup>
   <ItemGroup>
     <Content Include="zips\winzip-sfx.exe">
diff --git a/src/Zip Tests/zips/offset.bin b/src/Zip Tests/zips/offset.bin
new file mode 100644
index 0000000..d9fa011
Binary files /dev/null and b/src/Zip Tests/zips/offset.bin differ
diff --git a/src/Zip.Shared/OffsetStream.cs b/src/Zip.Shared/OffsetStream.cs
index 525019a..a846274 100644
--- a/src/Zip.Shared/OffsetStream.cs
+++ b/src/Zip.Shared/OffsetStream.cs
@@ -90,7 +90,18 @@ public override long Position
 
         public override long Seek(long offset, System.IO.SeekOrigin origin)
         {
-            return _innerStream.Seek(_originalPosition + offset, origin) - _originalPosition;
+            switch (origin)
+            {
+                case SeekOrigin.Begin:
+                    return _innerStream.Seek(_originalPosition + offset, origin) - _originalPosition;
+
+                case SeekOrigin.Current:
+                case SeekOrigin.End:
+                    return _innerStream.Seek(offset, origin) - _originalPosition;
+
+                default:
+                    throw new ArgumentOutOfRangeException(nameof(origin), origin, "Invalid seek origin");
+            }
         }